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Keywords:
completely regular semiring; skew-ring; b-lattice; archimedean semiring; additive separative semiring
completely regular semiring; skew-ring; b-lattice; archimedean semiring; additive separative semiring
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 additive separative.
References:
[1] Clifford A. H., Preston G. B.: The algebraic theory of semigroups. : Amer. Math. Soc., Providence Rhode Island, Vol. I. 1961. MR 0132791
[2] Grillet M. P.: Semirings with a completely simple additive semigroup. J. Austral. Math. Soc. A 20 (1975), 257–267. MR 0491843 | 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. MR 1704233
[4] Sen M. K., Maity S. K., Shum K. P.: On completely regular semirings. (submitted). Zbl 1115.16026
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