Morita equivalence for partially ordered monoids and po-\(\Gamma\)-semigroups with unities
We prove that operator pomonoids of a po-\(\Gamma\)-semigroup with unities are Morita equivalent pomonoids. Conversely, we show that if \(L\) and \(R\) are Morita equivalent pomonoids then a po-\(\Gamma\)-semigroup \(A\) with unities can be constructed such that left and right operator pomonoids of...
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| Дата: | 2018 |
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| Формат: | Стаття |
| Мова: | English |
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Lugansk National Taras Shevchenko University
2018
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| Онлайн доступ: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1058 |
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| Назва журналу: | Algebra and Discrete Mathematics |
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oai:ojs.admjournal.luguniv.edu.ua:article-10582018-04-26T02:40:33Z Morita equivalence for partially ordered monoids and po-\(\Gamma\)-semigroups with unities Gupta, Sugato Sardar, Sujit Kumar Morita equivalence for pomonoids, Morita invariant, Morita context, Po-\(\Gamma\)-semigroup 20M50, 06F05 We prove that operator pomonoids of a po-\(\Gamma\)-semigroup with unities are Morita equivalent pomonoids. Conversely, we show that if \(L\) and \(R\) are Morita equivalent pomonoids then a po-\(\Gamma\)-semigroup \(A\) with unities can be constructed such that left and right operator pomonoids of \(A\) are \(Pos\)-isomorphic to \(L\) and \(R\) respectively. Using this nice connection between po-\(\Gamma\)-semigroups and Morita equivalence for pomonoids we, in one hand, obtain some Morita invariants of pomonoids using the results of po-\(\Gamma\)-semigroups and on the other hand, some recent results of Morita theory of pomonoids are used to obtain some results of po-\(\Gamma\)-semigroups. Lugansk National Taras Shevchenko University 2018-04-26 Article Article Peer-reviewed Article application/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1058 Algebra and Discrete Mathematics; Vol 18, No 2 (2014) 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1058/580 Copyright (c) 2018 Algebra and Discrete Mathematics |
| institution |
Algebra and Discrete Mathematics |
| collection |
OJS |
| language |
English |
| topic |
Morita equivalence for pomonoids Morita invariant Morita context Po-\(\Gamma\)-semigroup 20M50 06F05 |
| spellingShingle |
Morita equivalence for pomonoids Morita invariant Morita context Po-\(\Gamma\)-semigroup 20M50 06F05 Gupta, Sugato Sardar, Sujit Kumar Morita equivalence for partially ordered monoids and po-\(\Gamma\)-semigroups with unities |
| topic_facet |
Morita equivalence for pomonoids Morita invariant Morita context Po-\(\Gamma\)-semigroup 20M50 06F05 |
| format |
Article |
| author |
Gupta, Sugato Sardar, Sujit Kumar |
| author_facet |
Gupta, Sugato Sardar, Sujit Kumar |
| author_sort |
Gupta, Sugato |
| title |
Morita equivalence for partially ordered monoids and po-\(\Gamma\)-semigroups with unities |
| title_short |
Morita equivalence for partially ordered monoids and po-\(\Gamma\)-semigroups with unities |
| title_full |
Morita equivalence for partially ordered monoids and po-\(\Gamma\)-semigroups with unities |
| title_fullStr |
Morita equivalence for partially ordered monoids and po-\(\Gamma\)-semigroups with unities |
| title_full_unstemmed |
Morita equivalence for partially ordered monoids and po-\(\Gamma\)-semigroups with unities |
| title_sort |
morita equivalence for partially ordered monoids and po-\(\gamma\)-semigroups with unities |
| description |
We prove that operator pomonoids of a po-\(\Gamma\)-semigroup with unities are Morita equivalent pomonoids. Conversely, we show that if \(L\) and \(R\) are Morita equivalent pomonoids then a po-\(\Gamma\)-semigroup \(A\) with unities can be constructed such that left and right operator pomonoids of \(A\) are \(Pos\)-isomorphic to \(L\) and \(R\) respectively. Using this nice connection between po-\(\Gamma\)-semigroups and Morita equivalence for pomonoids we, in one hand, obtain some Morita invariants of pomonoids using the results of po-\(\Gamma\)-semigroups and on the other hand, some recent results of Morita theory of pomonoids are used to obtain some results of po-\(\Gamma\)-semigroups. |
| publisher |
Lugansk National Taras Shevchenko University |
| publishDate |
2018 |
| url |
https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1058 |
| work_keys_str_mv |
AT guptasugato moritaequivalenceforpartiallyorderedmonoidsandpogammasemigroupswithunities AT sardarsujitkumar moritaequivalenceforpartiallyorderedmonoidsandpogammasemigroupswithunities |
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2024-04-12T06:25:59Z |
| last_indexed |
2024-04-12T06:25:59Z |
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1796109143130505216 |