Quasi \(k\)-ideals in \(k\)-regular and intra \(k\)-regular semirings. (English) Zbl 1249.16053

Jana, Kanchan

PU.M.A., Pure Math. Appl. 22, No. 1, 65-74 (2011).

Summary: A semiring \(S\) whose additive reduct is a semilattice, is called an intra \(k\)-regular semiring if for each \(a\in S\) there exists \(x\in S\) such that \(a+xa^2x=xa^2x\) and is called a \(k\)-regular semiring if for each \(a\in S\) there exists \(x\in S\) such that \(a+axa=axa\). Here we introduce quasi \(k\)-ideals in semirings and characterize both the \(k\)-regular and intra \(k\)-regular semirings by their quasi \(k\)-ideals.

MSC:

16Y60	Semirings
16D25	Ideals in associative algebras
16E50	von Neumann regular rings and generalizations (associative algebraic aspects)

Keywords:

quasi \(k\)-ideals; \(k\)-regular semirings; intra regular semirings