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Morita equivalence of semirings and its connection with Nobusawa \(\Gamma\)-semirings with unities. (English) Zbl 1333.16048

Summary: We show that the left operator semiring and the right operator semiring of a Nobusawa \(\Gamma\)-semiring with unities are Morita equivalent. The converse is also deduced, i.e., for two Morita equivalent semirings \(L\) and \(R\), a Nobusawa \(\Gamma\)-semiring \(A\) with unities is constructed such that the left and right operator semirings of \(A\) are isomorphic to \(L\) and \(R\), respectively. As an application we first establish a relationship between Morita equivalence and Morita context of semirings, and then enumerate some properties of semirings which remain invariant under Morita equivalence.

MSC:

16Y99 Generalizations
16Y60 Semirings
16D90 Module categories in associative algebras
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