Morita equivalence based on Morita context for arbitrary semigroups | Zendy

Hongxing Liu | Zendy

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Morita equivalence based on Morita context for arbitrary semigroups

Author(s) -

Hongxing Liu

Publication year - 2016

Publication title -

hacettepe journal of mathematics and statistics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.312

H-Index - 26

ISSN - 1303-5010

DOI - 10.15672/hjms.20164520080

Subject(s) - morita equivalence , morita therapy , mathematics , equivalence (formal languages) , context (archaeology) , pure mathematics , algebra over a field , paleontology , biology

In this paper, we study the Morita context for arbitrary semigroups. We prove that, for two semigroups S and T, if there exists a Morita context $(S, T, P, Q, \tau, \mu)$ (not necessary unital) such that the maps $\tau$ and $\mu$ are surjective, the categories U S -FAct and U T -FAct are equivalent. Using this result, we generalize Theorem 2 in [2] to arbitrary semigroups. Finally, we give a characterization of Morita context for semigroups.

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