Abstract
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.
Citation
M. K. Sen. S. K. Maity. K. P. Shum. "CLIFFORD SEMIRINGS AND GENERALIZED CLIFFORD SEMIRINGS." Taiwanese J. Math. 9 (3) 433 - 444, 2005. https://doi.org/10.11650/twjm/1500407851
Information