Very true operators on MTL-algebras

The main goal of this paper is to investigate very true MTL-algebras and prove the completeness of the very true MTL-logic. In this paper, the concept of very true operators on MTL-algebras is introduced and some related properties are investigated. Also, conditions for an MTL-algebra to be an MV-al...
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Autor*in:	Wang Jun Tao [verfasserIn] Xin Xiao Long [verfasserIn] Saeid Arsham Borumand [verfasserIn]

Format:	E-Artikel
Sprache:	Englisch

Erschienen:	2016

Schlagwörter:	very true mtl-algebra subdirectly irreducible representation stabilizer topology very true mtl-logic 03f50 06f99

Übergeordnetes Werk:	In: Open Mathematics - De Gruyter, 2015, 14(2016), 1, Seite 955-969
Übergeordnetes Werk:	volume:14 ; year:2016 ; number:1 ; pages:955-969

Links:	Link aufrufen Link aufrufen Link aufrufen Journal toc

DOI / URN:	10.1515/math-2016-0086

Katalog-ID:	DOAJ061840653

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520			\|a The main goal of this paper is to investigate very true MTL-algebras and prove the completeness of the very true MTL-logic. In this paper, the concept of very true operators on MTL-algebras is introduced and some related properties are investigated. Also, conditions for an MTL-algebra to be an MV-algebra and a Gödel algebra are given via this operator. Moreover, very true filters on very true MTL-algebras are studied. In particular, subdirectly irreducible very true MTL-algebras are characterized and an analogous of representation theorem for very true MTL-algebras is proved. Then, the left and right stabilizers of very true MTL-algebras are introduced and some related properties are given. As applications of stabilizer of very true MTL-algebras, we produce a basis for a topology on very true MTL-algebras and show that the generated topology by this basis is Baire, connected, locally connected and separable. Finally, the corresponding logic very true MTL-logic is constructed and the soundness and completeness of this logic are proved based on very true MTL-algebras.
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allfields	10.1515/math-2016-0086 doi (DE-627)DOAJ061840653 (DE-599)DOAJfdfccdf134bf46c5aa68bf2f37bd1f74 DE-627 ger DE-627 rakwb eng QA1-939 Wang Jun Tao verfasserin aut Very true operators on MTL-algebras 2016 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier The main goal of this paper is to investigate very true MTL-algebras and prove the completeness of the very true MTL-logic. In this paper, the concept of very true operators on MTL-algebras is introduced and some related properties are investigated. Also, conditions for an MTL-algebra to be an MV-algebra and a Gödel algebra are given via this operator. Moreover, very true filters on very true MTL-algebras are studied. In particular, subdirectly irreducible very true MTL-algebras are characterized and an analogous of representation theorem for very true MTL-algebras is proved. Then, the left and right stabilizers of very true MTL-algebras are introduced and some related properties are given. As applications of stabilizer of very true MTL-algebras, we produce a basis for a topology on very true MTL-algebras and show that the generated topology by this basis is Baire, connected, locally connected and separable. Finally, the corresponding logic very true MTL-logic is constructed and the soundness and completeness of this logic are proved based on very true MTL-algebras. very true mtl-algebra subdirectly irreducible representation stabilizer topology very true mtl-logic 03f50 06f99 Mathematics Xin Xiao Long verfasserin aut Saeid Arsham Borumand verfasserin aut In Open Mathematics De Gruyter, 2015 14(2016), 1, Seite 955-969 (DE-627)823698734 (DE-600)2818690-4 23915455 nnns volume:14 year:2016 number:1 pages:955-969 https://doi.org/10.1515/math-2016-0086 kostenfrei https://doaj.org/article/fdfccdf134bf46c5aa68bf2f37bd1f74 kostenfrei https://doi.org/10.1515/math-2016-0086 kostenfrei https://doaj.org/toc/2391-5455 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2014 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 14 2016 1 955-969
spelling	10.1515/math-2016-0086 doi (DE-627)DOAJ061840653 (DE-599)DOAJfdfccdf134bf46c5aa68bf2f37bd1f74 DE-627 ger DE-627 rakwb eng QA1-939 Wang Jun Tao verfasserin aut Very true operators on MTL-algebras 2016 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier The main goal of this paper is to investigate very true MTL-algebras and prove the completeness of the very true MTL-logic. In this paper, the concept of very true operators on MTL-algebras is introduced and some related properties are investigated. Also, conditions for an MTL-algebra to be an MV-algebra and a Gödel algebra are given via this operator. Moreover, very true filters on very true MTL-algebras are studied. In particular, subdirectly irreducible very true MTL-algebras are characterized and an analogous of representation theorem for very true MTL-algebras is proved. Then, the left and right stabilizers of very true MTL-algebras are introduced and some related properties are given. As applications of stabilizer of very true MTL-algebras, we produce a basis for a topology on very true MTL-algebras and show that the generated topology by this basis is Baire, connected, locally connected and separable. Finally, the corresponding logic very true MTL-logic is constructed and the soundness and completeness of this logic are proved based on very true MTL-algebras. very true mtl-algebra subdirectly irreducible representation stabilizer topology very true mtl-logic 03f50 06f99 Mathematics Xin Xiao Long verfasserin aut Saeid Arsham Borumand verfasserin aut In Open Mathematics De Gruyter, 2015 14(2016), 1, Seite 955-969 (DE-627)823698734 (DE-600)2818690-4 23915455 nnns volume:14 year:2016 number:1 pages:955-969 https://doi.org/10.1515/math-2016-0086 kostenfrei https://doaj.org/article/fdfccdf134bf46c5aa68bf2f37bd1f74 kostenfrei https://doi.org/10.1515/math-2016-0086 kostenfrei https://doaj.org/toc/2391-5455 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2014 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 14 2016 1 955-969
allfields_unstemmed	10.1515/math-2016-0086 doi (DE-627)DOAJ061840653 (DE-599)DOAJfdfccdf134bf46c5aa68bf2f37bd1f74 DE-627 ger DE-627 rakwb eng QA1-939 Wang Jun Tao verfasserin aut Very true operators on MTL-algebras 2016 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier The main goal of this paper is to investigate very true MTL-algebras and prove the completeness of the very true MTL-logic. In this paper, the concept of very true operators on MTL-algebras is introduced and some related properties are investigated. Also, conditions for an MTL-algebra to be an MV-algebra and a Gödel algebra are given via this operator. Moreover, very true filters on very true MTL-algebras are studied. In particular, subdirectly irreducible very true MTL-algebras are characterized and an analogous of representation theorem for very true MTL-algebras is proved. Then, the left and right stabilizers of very true MTL-algebras are introduced and some related properties are given. As applications of stabilizer of very true MTL-algebras, we produce a basis for a topology on very true MTL-algebras and show that the generated topology by this basis is Baire, connected, locally connected and separable. Finally, the corresponding logic very true MTL-logic is constructed and the soundness and completeness of this logic are proved based on very true MTL-algebras. very true mtl-algebra subdirectly irreducible representation stabilizer topology very true mtl-logic 03f50 06f99 Mathematics Xin Xiao Long verfasserin aut Saeid Arsham Borumand verfasserin aut In Open Mathematics De Gruyter, 2015 14(2016), 1, Seite 955-969 (DE-627)823698734 (DE-600)2818690-4 23915455 nnns volume:14 year:2016 number:1 pages:955-969 https://doi.org/10.1515/math-2016-0086 kostenfrei https://doaj.org/article/fdfccdf134bf46c5aa68bf2f37bd1f74 kostenfrei https://doi.org/10.1515/math-2016-0086 kostenfrei https://doaj.org/toc/2391-5455 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2014 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 14 2016 1 955-969
allfieldsGer	10.1515/math-2016-0086 doi (DE-627)DOAJ061840653 (DE-599)DOAJfdfccdf134bf46c5aa68bf2f37bd1f74 DE-627 ger DE-627 rakwb eng QA1-939 Wang Jun Tao verfasserin aut Very true operators on MTL-algebras 2016 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier The main goal of this paper is to investigate very true MTL-algebras and prove the completeness of the very true MTL-logic. In this paper, the concept of very true operators on MTL-algebras is introduced and some related properties are investigated. Also, conditions for an MTL-algebra to be an MV-algebra and a Gödel algebra are given via this operator. Moreover, very true filters on very true MTL-algebras are studied. In particular, subdirectly irreducible very true MTL-algebras are characterized and an analogous of representation theorem for very true MTL-algebras is proved. Then, the left and right stabilizers of very true MTL-algebras are introduced and some related properties are given. As applications of stabilizer of very true MTL-algebras, we produce a basis for a topology on very true MTL-algebras and show that the generated topology by this basis is Baire, connected, locally connected and separable. Finally, the corresponding logic very true MTL-logic is constructed and the soundness and completeness of this logic are proved based on very true MTL-algebras. very true mtl-algebra subdirectly irreducible representation stabilizer topology very true mtl-logic 03f50 06f99 Mathematics Xin Xiao Long verfasserin aut Saeid Arsham Borumand verfasserin aut In Open Mathematics De Gruyter, 2015 14(2016), 1, Seite 955-969 (DE-627)823698734 (DE-600)2818690-4 23915455 nnns volume:14 year:2016 number:1 pages:955-969 https://doi.org/10.1515/math-2016-0086 kostenfrei https://doaj.org/article/fdfccdf134bf46c5aa68bf2f37bd1f74 kostenfrei https://doi.org/10.1515/math-2016-0086 kostenfrei https://doaj.org/toc/2391-5455 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2014 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 14 2016 1 955-969
allfieldsSound	10.1515/math-2016-0086 doi (DE-627)DOAJ061840653 (DE-599)DOAJfdfccdf134bf46c5aa68bf2f37bd1f74 DE-627 ger DE-627 rakwb eng QA1-939 Wang Jun Tao verfasserin aut Very true operators on MTL-algebras 2016 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier The main goal of this paper is to investigate very true MTL-algebras and prove the completeness of the very true MTL-logic. In this paper, the concept of very true operators on MTL-algebras is introduced and some related properties are investigated. Also, conditions for an MTL-algebra to be an MV-algebra and a Gödel algebra are given via this operator. Moreover, very true filters on very true MTL-algebras are studied. In particular, subdirectly irreducible very true MTL-algebras are characterized and an analogous of representation theorem for very true MTL-algebras is proved. Then, the left and right stabilizers of very true MTL-algebras are introduced and some related properties are given. As applications of stabilizer of very true MTL-algebras, we produce a basis for a topology on very true MTL-algebras and show that the generated topology by this basis is Baire, connected, locally connected and separable. Finally, the corresponding logic very true MTL-logic is constructed and the soundness and completeness of this logic are proved based on very true MTL-algebras. very true mtl-algebra subdirectly irreducible representation stabilizer topology very true mtl-logic 03f50 06f99 Mathematics Xin Xiao Long verfasserin aut Saeid Arsham Borumand verfasserin aut In Open Mathematics De Gruyter, 2015 14(2016), 1, Seite 955-969 (DE-627)823698734 (DE-600)2818690-4 23915455 nnns volume:14 year:2016 number:1 pages:955-969 https://doi.org/10.1515/math-2016-0086 kostenfrei https://doaj.org/article/fdfccdf134bf46c5aa68bf2f37bd1f74 kostenfrei https://doi.org/10.1515/math-2016-0086 kostenfrei https://doaj.org/toc/2391-5455 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2014 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 14 2016 1 955-969
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source	In Open Mathematics 14(2016), 1, Seite 955-969 volume:14 year:2016 number:1 pages:955-969
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authorswithroles_txt_mv	Wang Jun Tao @@aut@@ Xin Xiao Long @@aut@@ Saeid Arsham Borumand @@aut@@
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author	Wang Jun Tao
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topic_title	QA1-939 Very true operators on MTL-algebras very true mtl-algebra subdirectly irreducible representation stabilizer topology very true mtl-logic 03f50 06f99
topic	misc QA1-939 misc very true mtl-algebra misc subdirectly irreducible misc representation misc stabilizer topology misc very true mtl-logic misc 03f50 misc 06f99 misc Mathematics
topic_unstemmed	misc QA1-939 misc very true mtl-algebra misc subdirectly irreducible misc representation misc stabilizer topology misc very true mtl-logic misc 03f50 misc 06f99 misc Mathematics
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title	Very true operators on MTL-algebras
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title_auth	Very true operators on MTL-algebras
abstract	The main goal of this paper is to investigate very true MTL-algebras and prove the completeness of the very true MTL-logic. In this paper, the concept of very true operators on MTL-algebras is introduced and some related properties are investigated. Also, conditions for an MTL-algebra to be an MV-algebra and a Gödel algebra are given via this operator. Moreover, very true filters on very true MTL-algebras are studied. In particular, subdirectly irreducible very true MTL-algebras are characterized and an analogous of representation theorem for very true MTL-algebras is proved. Then, the left and right stabilizers of very true MTL-algebras are introduced and some related properties are given. As applications of stabilizer of very true MTL-algebras, we produce a basis for a topology on very true MTL-algebras and show that the generated topology by this basis is Baire, connected, locally connected and separable. Finally, the corresponding logic very true MTL-logic is constructed and the soundness and completeness of this logic are proved based on very true MTL-algebras.
abstractGer	The main goal of this paper is to investigate very true MTL-algebras and prove the completeness of the very true MTL-logic. In this paper, the concept of very true operators on MTL-algebras is introduced and some related properties are investigated. Also, conditions for an MTL-algebra to be an MV-algebra and a Gödel algebra are given via this operator. Moreover, very true filters on very true MTL-algebras are studied. In particular, subdirectly irreducible very true MTL-algebras are characterized and an analogous of representation theorem for very true MTL-algebras is proved. Then, the left and right stabilizers of very true MTL-algebras are introduced and some related properties are given. As applications of stabilizer of very true MTL-algebras, we produce a basis for a topology on very true MTL-algebras and show that the generated topology by this basis is Baire, connected, locally connected and separable. Finally, the corresponding logic very true MTL-logic is constructed and the soundness and completeness of this logic are proved based on very true MTL-algebras.
abstract_unstemmed	The main goal of this paper is to investigate very true MTL-algebras and prove the completeness of the very true MTL-logic. In this paper, the concept of very true operators on MTL-algebras is introduced and some related properties are investigated. Also, conditions for an MTL-algebra to be an MV-algebra and a Gödel algebra are given via this operator. Moreover, very true filters on very true MTL-algebras are studied. In particular, subdirectly irreducible very true MTL-algebras are characterized and an analogous of representation theorem for very true MTL-algebras is proved. Then, the left and right stabilizers of very true MTL-algebras are introduced and some related properties are given. As applications of stabilizer of very true MTL-algebras, we produce a basis for a topology on very true MTL-algebras and show that the generated topology by this basis is Baire, connected, locally connected and separable. Finally, the corresponding logic very true MTL-logic is constructed and the soundness and completeness of this logic are proved based on very true MTL-algebras.
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tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4305</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4306</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4307</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4313</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4322</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4323</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4324</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4325</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4326</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4335</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4338</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4367</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4700</subfield></datafield><datafield tag="951" ind1=" " ind2=" "><subfield code="a">AR</subfield></datafield><datafield tag="952" ind1=" " ind2=" "><subfield code="d">14</subfield><subfield code="j">2016</subfield><subfield code="e">1</subfield><subfield code="h">955-969</subfield></datafield></record></collection>
score	7.400079

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