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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.

MSC:

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

[1] Clifford A. H., Preston G. B.: The algebraic theory of semigroups. : Amer. Math. Soc., Providence Rhode Island, Vol. I. 1961.
[2] Grillet M. P.: Semirings with a completely simple additive semigroup. J. Austral. Math. Soc. A 20 (1975), 257-267. · Zbl 0316.16039
[3] Hebisch, U, Weinert H. J.: Semirings, Algebra Theory, Applications in Computer Science, Series in Algebra. : Vol. 5, World Scientific, Singapore. 1998. · Zbl 0934.16046
[4] Sen M. K., Maity S. K., Shum K. P.: On completely regular semirings. · Zbl 1115.16026
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