Morita invariants of semirings. (Q2788562)

The authors study the Morita equivalence for semirings. This has been introduced by \textit{Y. Katsov} and \textit{T. G. Nam} [in the paper J. Algebra Appl. 10, No. 3, 445-473 (2011; Zbl 1250.16031)].NEWLINENEWLINE The main results are: 1. Let \(R\) and \(S\) be Morita equivalent semirings. Then \(R\) is additively cancellative (additively idempotent, additively regular, zero-sum free) if and only if \(S\) is so. 2. The lattices of \(k\)-ideals (\(h\)-ideals) of two Morita equivalent semirings are isomorphic. 3. The canonical maps preserve finitely generated ideals, prime ideals, primary ideals for two Morita equivalent semirings. 4. Two Morita equivalent semirings are simultaneously Noether and their lattices of congruences are isomorphic.