Semirings embedded in a completely regular semiring. (English) Zbl 1067.16069

Summary: Recently, we have shown that a semiring \(S\) is completely regular if and only if \(S\) is a union of skew-rings. In this paper we show that a semiring \(S\) satisfying \(a^2=na\) can be embedded in a completely regular semiring if and only if \(S\) is additively separative.


16Y60 Semirings
16E50 von Neumann regular rings and generalizations (associative algebraic aspects)
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