Purely Infinite Simple Ultragraph Leavitt Path Algebras
Abstract In this article, we give necessary and sufficient conditions under which the Leavitt path algebra $$L_K(\mathcal {G})$$ of an ultragraph $$\mathcal {G}$$ over a field K is purely infinite simple and that it is von Neumann regular. Consequently, we obtain that every graded simple ultragraph...
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Gespeichert in:
| Autor*in: |
Nam, T. G. [verfasserIn] |
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| Format: |
Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2021 |
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| Schlagwörter: |
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| Anmerkung: |
© The Author(s), under exclusive licence to Springer Nature Switzerland AG 2021 |
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| Übergeordnetes Werk: |
Enthalten in: Mediterranean journal of mathematics - Springer International Publishing, 2004, 19(2021), 1 vom: 22. Nov. |
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| Übergeordnetes Werk: |
volume:19 ; year:2021 ; number:1 ; day:22 ; month:11 |
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| DOI / URN: |
10.1007/s00009-021-01899-y |
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| 520 | |a Abstract In this article, we give necessary and sufficient conditions under which the Leavitt path algebra $$L_K(\mathcal {G})$$ of an ultragraph $$\mathcal {G}$$ over a field K is purely infinite simple and that it is von Neumann regular. Consequently, we obtain that every graded simple ultragraph Leavitt path algebra is either a locally matricial algebra, or a full matrix ring over $$K[x, x^{-1}]$$, or a purely infinite simple algebra. | ||
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| 650 | 4 | |a purely infinite simplicity | |
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| 650 | 4 | |a von Neumann regularity | |
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10.1007/s00009-021-01899-y doi (DE-627)OLC2077501480 (DE-He213)s00009-021-01899-y-p DE-627 ger DE-627 rakwb eng 510 VZ 17,1 ssgn Nam, T. G. verfasserin aut Purely Infinite Simple Ultragraph Leavitt Path Algebras 2021 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © The Author(s), under exclusive licence to Springer Nature Switzerland AG 2021 Abstract In this article, we give necessary and sufficient conditions under which the Leavitt path algebra $$L_K(\mathcal {G})$$ of an ultragraph $$\mathcal {G}$$ over a field K is purely infinite simple and that it is von Neumann regular. Consequently, we obtain that every graded simple ultragraph Leavitt path algebra is either a locally matricial algebra, or a full matrix ring over $$K[x, x^{-1}]$$, or a purely infinite simple algebra. Ultragraph Leavitt path algebras purely infinite simplicity graded simplicity von Neumann regularity Nam, N. D. (orcid)0000-0002-7198-8787 aut Enthalten in Mediterranean journal of mathematics Springer International Publishing, 2004 19(2021), 1 vom: 22. Nov. (DE-627)389869848 (DE-600)2149653-5 (DE-576)12119308X 1660-5446 nnns volume:19 year:2021 number:1 day:22 month:11 https://doi.org/10.1007/s00009-021-01899-y lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_2088 AR 19 2021 1 22 11 |
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Abstract In this article, we give necessary and sufficient conditions under which the Leavitt path algebra $$L_K(\mathcal {G})$$ of an ultragraph $$\mathcal {G}$$ over a field K is purely infinite simple and that it is von Neumann regular. Consequently, we obtain that every graded simple ultragraph Leavitt path algebra is either a locally matricial algebra, or a full matrix ring over $$K[x, x^{-1}]$$, or a purely infinite simple algebra. © The Author(s), under exclusive licence to Springer Nature Switzerland AG 2021 |
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Abstract In this article, we give necessary and sufficient conditions under which the Leavitt path algebra $$L_K(\mathcal {G})$$ of an ultragraph $$\mathcal {G}$$ over a field K is purely infinite simple and that it is von Neumann regular. Consequently, we obtain that every graded simple ultragraph Leavitt path algebra is either a locally matricial algebra, or a full matrix ring over $$K[x, x^{-1}]$$, or a purely infinite simple algebra. © The Author(s), under exclusive licence to Springer Nature Switzerland AG 2021 |
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Abstract In this article, we give necessary and sufficient conditions under which the Leavitt path algebra $$L_K(\mathcal {G})$$ of an ultragraph $$\mathcal {G}$$ over a field K is purely infinite simple and that it is von Neumann regular. Consequently, we obtain that every graded simple ultragraph Leavitt path algebra is either a locally matricial algebra, or a full matrix ring over $$K[x, x^{-1}]$$, or a purely infinite simple algebra. © The Author(s), under exclusive licence to Springer Nature Switzerland AG 2021 |
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<?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01000caa a22002652 4500</leader><controlfield tag="001">OLC2077501480</controlfield><controlfield tag="003">DE-627</controlfield><controlfield tag="005">20230505224851.0</controlfield><controlfield tag="007">tu</controlfield><controlfield tag="008">221220s2021 xx ||||| 00| ||eng c</controlfield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1007/s00009-021-01899-y</subfield><subfield code="2">doi</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-627)OLC2077501480</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-He213)s00009-021-01899-y-p</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-627</subfield><subfield code="b">ger</subfield><subfield code="c">DE-627</subfield><subfield code="e">rakwb</subfield></datafield><datafield tag="041" ind1=" " ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="082" ind1="0" ind2="4"><subfield code="a">510</subfield><subfield code="q">VZ</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">17,1</subfield><subfield code="2">ssgn</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Nam, T. G.</subfield><subfield code="e">verfasserin</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Purely Infinite Simple Ultragraph Leavitt Path Algebras</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="c">2021</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="a">Text</subfield><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="a">ohne Hilfsmittel zu benutzen</subfield><subfield code="b">n</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="a">Band</subfield><subfield code="b">nc</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">© The Author(s), under exclusive licence to Springer Nature Switzerland AG 2021</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">Abstract In this article, we give necessary and sufficient conditions under which the Leavitt path algebra $$L_K(\mathcal {G})$$ of an ultragraph $$\mathcal {G}$$ over a field K is purely infinite simple and that it is von Neumann regular. Consequently, we obtain that every graded simple ultragraph Leavitt path algebra is either a locally matricial algebra, or a full matrix ring over $$K[x, x^{-1}]$$, or a purely infinite simple algebra.</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Ultragraph Leavitt path algebras</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">purely infinite simplicity</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">graded simplicity</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">von Neumann regularity</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Nam, N. D.</subfield><subfield code="0">(orcid)0000-0002-7198-8787</subfield><subfield code="4">aut</subfield></datafield><datafield tag="773" ind1="0" ind2="8"><subfield code="i">Enthalten in</subfield><subfield code="t">Mediterranean journal of mathematics</subfield><subfield code="d">Springer International Publishing, 2004</subfield><subfield code="g">19(2021), 1 vom: 22. 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