Abstract
A U-abundant semigroup S in which every \( \mathcal{H} \)-class of S contains an element in the set of projections U of S is said to be a U-superabundant semigroup. This is an analogue of regular semigroups which are unions of groups and an analogue of abundant semigroups which are superabundant. In 1941, Clifford proved that a semigroup is a union of groups if and only if it is a semilattice of completely simple semigroups. Several years later, Fountain generalized this result to the class of superabundant semigroups. In this paper, we extend their work to U-superabundant semigroups.
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Ren, X., Shum, K.P. & Guo, Y. A generalized Clifford theorem of semigroups. Sci. China Math. 53, 1097–1101 (2010). https://doi.org/10.1007/s11425-009-0150-3
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DOI: https://doi.org/10.1007/s11425-009-0150-3
Keywords
- Clifford theorem
- unions of groups
- superabundant semigroups
- U-abundant semigroups
- U-superabundant semigroups