Cartesian product of compressible effect algebras
Abstract In the paper, we prove that $$C(p)=\{a\in E\mid a $$ is compatible with p}, the set of commutant of p, and $$C_p(a)=\{p\in P(E)\mid a=J_p(a)\oplus J_{p'}(a)\}=\{p\in P(E)\mid a\in C(p)\}$$ , the projection commutant of a, are all normal sub-effect algebras of a compressible effect alge...
Ausführliche Beschreibung
Gespeichert in:
| Autor*in: |
Li, Hai-Yang [verfasserIn] |
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| Format: |
Artikel |
|---|---|
| Sprache: |
Englisch |
| Erschienen: |
2008 |
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| Schlagwörter: |
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| Anmerkung: |
© Springer-Verlag 2008 |
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| Übergeordnetes Werk: |
Enthalten in: Soft computing - Springer-Verlag, 1997, 12(2008), 11 vom: 05. Feb., Seite 1115-1118 |
|---|---|
| Übergeordnetes Werk: |
volume:12 ; year:2008 ; number:11 ; day:05 ; month:02 ; pages:1115-1118 |
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| DOI / URN: |
10.1007/s00500-008-0279-y |
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OLC2034867378 |
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| 520 | |a Abstract In the paper, we prove that $$C(p)=\{a\in E\mid a $$ is compatible with p}, the set of commutant of p, and $$C_p(a)=\{p\in P(E)\mid a=J_p(a)\oplus J_{p'}(a)\}=\{p\in P(E)\mid a\in C(p)\}$$ , the projection commutant of a, are all normal sub-effect algebras of a compressible effect algebra E, and $$Q = \{q\mid J_q$$ is a direct retraction on E} is a normal sub-effect algebra of an effect algebra E. Moreover, we answer an open question in Gudder’s (Rep Math Phys 54:93–114, 2004), Compressible effect algebras, Rep Math Phys, by showing that the cartesian product of an infinite number of Ei is a compressible effect algebra if and only if each Ei is a compressible effect algebra. | ||
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| 650 | 4 | |a Compressible effect algebras | |
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| 700 | 1 | |a Zhu, Min-Hui |4 aut | |
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10.1007/s00500-008-0279-y doi (DE-627)OLC2034867378 (DE-He213)s00500-008-0279-y-p DE-627 ger DE-627 rakwb eng 004 VZ 004 VZ 11 ssgn Li, Hai-Yang verfasserin aut Cartesian product of compressible effect algebras 2008 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer-Verlag 2008 Abstract In the paper, we prove that $$C(p)=\{a\in E\mid a $$ is compatible with p}, the set of commutant of p, and $$C_p(a)=\{p\in P(E)\mid a=J_p(a)\oplus J_{p'}(a)\}=\{p\in P(E)\mid a\in C(p)\}$$ , the projection commutant of a, are all normal sub-effect algebras of a compressible effect algebra E, and $$Q = \{q\mid J_q$$ is a direct retraction on E} is a normal sub-effect algebra of an effect algebra E. Moreover, we answer an open question in Gudder’s (Rep Math Phys 54:93–114, 2004), Compressible effect algebras, Rep Math Phys, by showing that the cartesian product of an infinite number of Ei is a compressible effect algebra if and only if each Ei is a compressible effect algebra. Effect algebras Compressible effect algebras Normal sub-effect algebras Cartesian product Li, Sheng-Gang aut Zhu, Min-Hui aut Enthalten in Soft computing Springer-Verlag, 1997 12(2008), 11 vom: 05. Feb., Seite 1115-1118 (DE-627)231970536 (DE-600)1387526-7 (DE-576)060238259 1432-7643 nnns volume:12 year:2008 number:11 day:05 month:02 pages:1115-1118 https://doi.org/10.1007/s00500-008-0279-y lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT GBV_ILN_40 GBV_ILN_70 GBV_ILN_267 GBV_ILN_2018 GBV_ILN_4277 AR 12 2008 11 05 02 1115-1118 |
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10.1007/s00500-008-0279-y doi (DE-627)OLC2034867378 (DE-He213)s00500-008-0279-y-p DE-627 ger DE-627 rakwb eng 004 VZ 004 VZ 11 ssgn Li, Hai-Yang verfasserin aut Cartesian product of compressible effect algebras 2008 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer-Verlag 2008 Abstract In the paper, we prove that $$C(p)=\{a\in E\mid a $$ is compatible with p}, the set of commutant of p, and $$C_p(a)=\{p\in P(E)\mid a=J_p(a)\oplus J_{p'}(a)\}=\{p\in P(E)\mid a\in C(p)\}$$ , the projection commutant of a, are all normal sub-effect algebras of a compressible effect algebra E, and $$Q = \{q\mid J_q$$ is a direct retraction on E} is a normal sub-effect algebra of an effect algebra E. Moreover, we answer an open question in Gudder’s (Rep Math Phys 54:93–114, 2004), Compressible effect algebras, Rep Math Phys, by showing that the cartesian product of an infinite number of Ei is a compressible effect algebra if and only if each Ei is a compressible effect algebra. Effect algebras Compressible effect algebras Normal sub-effect algebras Cartesian product Li, Sheng-Gang aut Zhu, Min-Hui aut Enthalten in Soft computing Springer-Verlag, 1997 12(2008), 11 vom: 05. Feb., Seite 1115-1118 (DE-627)231970536 (DE-600)1387526-7 (DE-576)060238259 1432-7643 nnns volume:12 year:2008 number:11 day:05 month:02 pages:1115-1118 https://doi.org/10.1007/s00500-008-0279-y lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT GBV_ILN_40 GBV_ILN_70 GBV_ILN_267 GBV_ILN_2018 GBV_ILN_4277 AR 12 2008 11 05 02 1115-1118 |
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10.1007/s00500-008-0279-y doi (DE-627)OLC2034867378 (DE-He213)s00500-008-0279-y-p DE-627 ger DE-627 rakwb eng 004 VZ 004 VZ 11 ssgn Li, Hai-Yang verfasserin aut Cartesian product of compressible effect algebras 2008 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer-Verlag 2008 Abstract In the paper, we prove that $$C(p)=\{a\in E\mid a $$ is compatible with p}, the set of commutant of p, and $$C_p(a)=\{p\in P(E)\mid a=J_p(a)\oplus J_{p'}(a)\}=\{p\in P(E)\mid a\in C(p)\}$$ , the projection commutant of a, are all normal sub-effect algebras of a compressible effect algebra E, and $$Q = \{q\mid J_q$$ is a direct retraction on E} is a normal sub-effect algebra of an effect algebra E. Moreover, we answer an open question in Gudder’s (Rep Math Phys 54:93–114, 2004), Compressible effect algebras, Rep Math Phys, by showing that the cartesian product of an infinite number of Ei is a compressible effect algebra if and only if each Ei is a compressible effect algebra. Effect algebras Compressible effect algebras Normal sub-effect algebras Cartesian product Li, Sheng-Gang aut Zhu, Min-Hui aut Enthalten in Soft computing Springer-Verlag, 1997 12(2008), 11 vom: 05. Feb., Seite 1115-1118 (DE-627)231970536 (DE-600)1387526-7 (DE-576)060238259 1432-7643 nnns volume:12 year:2008 number:11 day:05 month:02 pages:1115-1118 https://doi.org/10.1007/s00500-008-0279-y lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT GBV_ILN_40 GBV_ILN_70 GBV_ILN_267 GBV_ILN_2018 GBV_ILN_4277 AR 12 2008 11 05 02 1115-1118 |
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10.1007/s00500-008-0279-y doi (DE-627)OLC2034867378 (DE-He213)s00500-008-0279-y-p DE-627 ger DE-627 rakwb eng 004 VZ 004 VZ 11 ssgn Li, Hai-Yang verfasserin aut Cartesian product of compressible effect algebras 2008 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer-Verlag 2008 Abstract In the paper, we prove that $$C(p)=\{a\in E\mid a $$ is compatible with p}, the set of commutant of p, and $$C_p(a)=\{p\in P(E)\mid a=J_p(a)\oplus J_{p'}(a)\}=\{p\in P(E)\mid a\in C(p)\}$$ , the projection commutant of a, are all normal sub-effect algebras of a compressible effect algebra E, and $$Q = \{q\mid J_q$$ is a direct retraction on E} is a normal sub-effect algebra of an effect algebra E. Moreover, we answer an open question in Gudder’s (Rep Math Phys 54:93–114, 2004), Compressible effect algebras, Rep Math Phys, by showing that the cartesian product of an infinite number of Ei is a compressible effect algebra if and only if each Ei is a compressible effect algebra. Effect algebras Compressible effect algebras Normal sub-effect algebras Cartesian product Li, Sheng-Gang aut Zhu, Min-Hui aut Enthalten in Soft computing Springer-Verlag, 1997 12(2008), 11 vom: 05. Feb., Seite 1115-1118 (DE-627)231970536 (DE-600)1387526-7 (DE-576)060238259 1432-7643 nnns volume:12 year:2008 number:11 day:05 month:02 pages:1115-1118 https://doi.org/10.1007/s00500-008-0279-y lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT GBV_ILN_40 GBV_ILN_70 GBV_ILN_267 GBV_ILN_2018 GBV_ILN_4277 AR 12 2008 11 05 02 1115-1118 |
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10.1007/s00500-008-0279-y doi (DE-627)OLC2034867378 (DE-He213)s00500-008-0279-y-p DE-627 ger DE-627 rakwb eng 004 VZ 004 VZ 11 ssgn Li, Hai-Yang verfasserin aut Cartesian product of compressible effect algebras 2008 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer-Verlag 2008 Abstract In the paper, we prove that $$C(p)=\{a\in E\mid a $$ is compatible with p}, the set of commutant of p, and $$C_p(a)=\{p\in P(E)\mid a=J_p(a)\oplus J_{p'}(a)\}=\{p\in P(E)\mid a\in C(p)\}$$ , the projection commutant of a, are all normal sub-effect algebras of a compressible effect algebra E, and $$Q = \{q\mid J_q$$ is a direct retraction on E} is a normal sub-effect algebra of an effect algebra E. Moreover, we answer an open question in Gudder’s (Rep Math Phys 54:93–114, 2004), Compressible effect algebras, Rep Math Phys, by showing that the cartesian product of an infinite number of Ei is a compressible effect algebra if and only if each Ei is a compressible effect algebra. Effect algebras Compressible effect algebras Normal sub-effect algebras Cartesian product Li, Sheng-Gang aut Zhu, Min-Hui aut Enthalten in Soft computing Springer-Verlag, 1997 12(2008), 11 vom: 05. Feb., Seite 1115-1118 (DE-627)231970536 (DE-600)1387526-7 (DE-576)060238259 1432-7643 nnns volume:12 year:2008 number:11 day:05 month:02 pages:1115-1118 https://doi.org/10.1007/s00500-008-0279-y lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT GBV_ILN_40 GBV_ILN_70 GBV_ILN_267 GBV_ILN_2018 GBV_ILN_4277 AR 12 2008 11 05 02 1115-1118 |
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Abstract In the paper, we prove that $$C(p)=\{a\in E\mid a $$ is compatible with p}, the set of commutant of p, and $$C_p(a)=\{p\in P(E)\mid a=J_p(a)\oplus J_{p'}(a)\}=\{p\in P(E)\mid a\in C(p)\}$$ , the projection commutant of a, are all normal sub-effect algebras of a compressible effect algebra E, and $$Q = \{q\mid J_q$$ is a direct retraction on E} is a normal sub-effect algebra of an effect algebra E. Moreover, we answer an open question in Gudder’s (Rep Math Phys 54:93–114, 2004), Compressible effect algebras, Rep Math Phys, by showing that the cartesian product of an infinite number of Ei is a compressible effect algebra if and only if each Ei is a compressible effect algebra. © Springer-Verlag 2008 |
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Abstract In the paper, we prove that $$C(p)=\{a\in E\mid a $$ is compatible with p}, the set of commutant of p, and $$C_p(a)=\{p\in P(E)\mid a=J_p(a)\oplus J_{p'}(a)\}=\{p\in P(E)\mid a\in C(p)\}$$ , the projection commutant of a, are all normal sub-effect algebras of a compressible effect algebra E, and $$Q = \{q\mid J_q$$ is a direct retraction on E} is a normal sub-effect algebra of an effect algebra E. Moreover, we answer an open question in Gudder’s (Rep Math Phys 54:93–114, 2004), Compressible effect algebras, Rep Math Phys, by showing that the cartesian product of an infinite number of Ei is a compressible effect algebra if and only if each Ei is a compressible effect algebra. © Springer-Verlag 2008 |
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Abstract In the paper, we prove that $$C(p)=\{a\in E\mid a $$ is compatible with p}, the set of commutant of p, and $$C_p(a)=\{p\in P(E)\mid a=J_p(a)\oplus J_{p'}(a)\}=\{p\in P(E)\mid a\in C(p)\}$$ , the projection commutant of a, are all normal sub-effect algebras of a compressible effect algebra E, and $$Q = \{q\mid J_q$$ is a direct retraction on E} is a normal sub-effect algebra of an effect algebra E. Moreover, we answer an open question in Gudder’s (Rep Math Phys 54:93–114, 2004), Compressible effect algebras, Rep Math Phys, by showing that the cartesian product of an infinite number of Ei is a compressible effect algebra if and only if each Ei is a compressible effect algebra. © Springer-Verlag 2008 |
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Cartesian product of compressible effect algebras |
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Li, Sheng-Gang Zhu, Min-Hui |
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