Band decompositions of semigroups
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- by Mohan S. Putcha and Julian Weissglass PDF
- Proc. Amer. Math. Soc. 33 (1972), 1-7 Request permission
Abstract:
The existence of a band decomposition of a semigroup into semigroups having at most one idempotent and a group ideal whenever it has an idempotent is investigated. It is shown that S has such a band decomposition if and only if, for every c, $d \in {S^1},a \in S$, the idempotent multiples of cad and $c{a^2}d$ coincide. The main result is used to characterize those semigroups which are bands of groups, extending a theorem of Clifford.References
- A. H. Clifford, Bands of semigroups, Proc. Amer. Math. Soc. 5 (1954), 499–504. MR 62119, DOI 10.1090/S0002-9939-1954-0062119-9
- A. H. Clifford and G. B. Preston, The algebraic theory of semigroups. Vol. I, Mathematical Surveys, No. 7, American Mathematical Society, Providence, R.I., 1961. MR 0132791
- Mohan S. Putcha and Julian Weissglass, A semilattice decomposition into semigroups having at most one idempotent, Pacific J. Math. 39 (1971), 225–228. MR 304523
Additional Information
- © Copyright 1972 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 33 (1972), 1-7
- MSC: Primary 20M10
- DOI: https://doi.org/10.1090/S0002-9939-1972-0291335-7
- MathSciNet review: 0291335