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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| Datum: | 2018 |
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| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | English |
| Veröffentlicht: |
Lugansk National Taras Shevchenko University
2018
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| Schlagworte: | |
| Online Zugang: | 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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Algebra and Discrete Mathematics| Zusammenfassung: | 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. |
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