Document Zbl 1206.16047

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Characterization of regular semirings. (English) Zbl 1206.16047

Mat. Vesn. 48, No. 3-4, 83-85 (1996).

The author obtains the following two necessary and sufficient conditions for a commutative semiring \(R\) to be regular: \(R\) contains \(1\neq 0\) and the semiring of its \(k\)-ideals is regular; every \(k\)-ideal of \(R\) is semiprime.

Reviewer: Dragana Todorić (Beograd)

Cited in 2 Documents

MSC:

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

Keywords:

regular semirings; commutative semirings; semiprime \(k\)-ideals

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