A Note on Locally Inverse Semigroup Algebras
Let R be a commutative ring and S a finite locally inverse semigroup. It is proved that the semigroup algebra R[S] is isomorphic to the direct product of Munn algebras ℳ(R[GJ],mJ,nJ;PJ) with J∈S/𝒥, where mJ is the number of ℛ-classes in J, nJ the number of ℒ-classes in J, and GJ a maximu...
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| Format: | Article |
| Language: | English |
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Wiley
2008-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/2008/576061 |
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| _version_ | 1849410042460110848 |
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| author | Xiaojiang Guo |
| author_facet | Xiaojiang Guo |
| author_sort | Xiaojiang Guo |
| collection | DOAJ |
| description | Let R be a commutative ring and S a finite locally inverse semigroup. It is proved that the semigroup algebra R[S] is isomorphic to the direct product of Munn algebras ℳ(R[GJ],mJ,nJ;PJ) with J∈S/𝒥, where mJ is the number of ℛ-classes in J, nJ the number of ℒ-classes in J, and GJ a maximum subgroup of J. As applications, we obtain the sufficient and necessary conditions for the semigroup algebra of a finite locally inverse semigroup to be semisimple. |
| format | Article |
| id | doaj-art-7d61136bf9894ede92f0a292d24daa2e |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2008-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-7d61136bf9894ede92f0a292d24daa2e2025-08-20T03:35:18ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252008-01-01200810.1155/2008/576061576061A Note on Locally Inverse Semigroup AlgebrasXiaojiang Guo0Department of Mathematics, Jiangxi Normal University, Nanchang, Jiangxi 330022, ChinaLet R be a commutative ring and S a finite locally inverse semigroup. It is proved that the semigroup algebra R[S] is isomorphic to the direct product of Munn algebras ℳ(R[GJ],mJ,nJ;PJ) with J∈S/𝒥, where mJ is the number of ℛ-classes in J, nJ the number of ℒ-classes in J, and GJ a maximum subgroup of J. As applications, we obtain the sufficient and necessary conditions for the semigroup algebra of a finite locally inverse semigroup to be semisimple.http://dx.doi.org/10.1155/2008/576061 |
| spellingShingle | Xiaojiang Guo A Note on Locally Inverse Semigroup Algebras International Journal of Mathematics and Mathematical Sciences |
| title | A Note on Locally Inverse Semigroup Algebras |
| title_full | A Note on Locally Inverse Semigroup Algebras |
| title_fullStr | A Note on Locally Inverse Semigroup Algebras |
| title_full_unstemmed | A Note on Locally Inverse Semigroup Algebras |
| title_short | A Note on Locally Inverse Semigroup Algebras |
| title_sort | note on locally inverse semigroup algebras |
| url | http://dx.doi.org/10.1155/2008/576061 |
| work_keys_str_mv | AT xiaojiangguo anoteonlocallyinversesemigroupalgebras AT xiaojiangguo noteonlocallyinversesemigroupalgebras |