Sardar, Sujit Kumar; Gupta, Sugato; Saha, Bibhas Chandra Morita equivalence of semirings and its connection with Nobusawa \(\Gamma\)-semirings with unities. (English) Zbl 1333.16048 Algebra Colloq. 22, Spec. Iss. 1, 985-1000 (2015). 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. Cited in 6 Documents MSC: 16Y99 Generalizations 16Y60 Semirings 16D90 Module categories in associative algebras Keywords:Morita equivalences; Morita contexts; Morita invariants; Nobusawa \(\Gamma\)-semirings; operator semirings PDFBibTeX XMLCite \textit{S. K. Sardar} et al., Algebra Colloq. 22, 985--1000 (2015; Zbl 1333.16048) Full Text: DOI References: [1] Dutta M.L, Southeast Asian Bull. Math. 35 (3) pp 389– (2011) [2] Dutta S.K, S.) 46 pp 319– (2000) [3] Dutta S.K, Novi Sad J. Math. 30 (1) pp 97– (2000) [4] DOI: 10.1007/s100120200041 · Zbl 1035.16039 [5] Dutta S.K, Bull. Calcutta Math. Soc. 95 (2) pp 113– (2003) [6] Katsov, Algebra Colloquium 4 (2) pp 121– (1997) [7] DOI: 10.1142/S0219498811004793 · Zbl 1250.16031 [8] Nobusawa, Osaka J. Math 1 pp 81– (1964) [9] Rao, Southeast Asian Bull. Math. 19 pp 49– (1995) [10] Rao, Southeast Asian Bull. Math. 21 pp 281– (1997) [11] Sardar, Novi Sad J. Math. 35 (1) pp 1– (2005) [12] Sardar U., Novi Sad J. Math. 34 (1) pp 1– (2004) [13] Sardar B.C., Ser. Mat. Univ. Bacu 18 pp 283– (2008) [14] Sardar B.C, Int. J. Pure Appl. Math. 54 (3) pp 321– (2009) [15] Sardar B.C., International Journal of Algebra 4 (5) pp 209– (2010) [16] DOI: 10.1090/S0002-9904-1934-06003-8 · Zbl 0010.38804 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.