Sen, M. K.; Maity, S. K. Regular additively inverse semirings. (English) Zbl 1160.16309 Acta Math. Univ. Comen., New Ser. 75, No. 1, 137-146 (2006). Summary: We show that in a regular additively inverse semiring \((S,+,\cdot)\) with 1 satisfying the conditions (A) \(a(a+a')=a+a'\), (B) \(a(b+b')=(b+b')a\) and (C) \(a+a(b+b')=a\), for all \(a,b\in S\), the sum of two principal left ideals is again a principal left ideal. Also, we decompose \(S\) as a direct sum of two mutually inverse ideals. MSC: 16Y60 Semirings 16D25 Ideals in associative algebras 16E50 von Neumann regular rings and generalizations (associative algebraic aspects) Keywords:additively inverse semirings; regular semirings; principal left ideals; inverse ideals PDFBibTeX XMLCite \textit{M. K. Sen} and \textit{S. K. Maity}, Acta Math. Univ. Comen., New Ser. 75, No. 1, 137--146 (2006; Zbl 1160.16309) Full Text: EuDML