Taiwanese Journal of Mathematics


M. K. Sen, S. K. Maity, and K. P. Shum

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It is well known that a semigroup $S$ is a Clifford semigroup if and only if $S$ is a strong semilattice of groups. In this paper, we extend this important result from semigroups to semirings by showing that a semiring $S$ is a Clifford semiring if and only if $S$ is a strong distributive lattice of skew-rings. Also, as a further generalization, we prove that a semiring $S$ is a genneralized Clifford semiring if and only if $S$ is a strong b-lattice of skew-rings. Some results which have been recently obtained in the literature [2] are strengthened and extended.

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Taiwanese J. Math., Volume 9, Number 3 (2005), 433-444.

First available in Project Euclid: 18 July 2017

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Zentralblatt MATH identifier

Primary: 16A78 20M07: Varieties and pseudovarieties of semigroups

completely regular semiring Clifford semiring generalized Clifford semiring skew-ring b-lattice


Sen, M. K.; Maity, S. K.; Shum, K. P. CLIFFORD SEMIRINGS AND GENERALIZED CLIFFORD SEMIRINGS. Taiwanese J. Math. 9 (2005), no. 3, 433--444. doi:10.11650/twjm/1500407851. https://projecteuclid.org/euclid.twjm/1500407851

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