On the structure of idempotent semigroups
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- by R. J. Warne
- Proc. Amer. Math. Soc. 37 (1973), 17-21
- DOI: https://doi.org/10.1090/S0002-9939-1973-0306380-3
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Abstract:
An idempotent semigroup (band) is a semigroup in which every element is an idempotent. We describe the structure of idempotent semigroups in terms of semilattices $\Omega$, partial chains $\Omega$ of left zero semigroups, and partial chains $\Omega$ of right zero semigroups. We also describe bands of maximal left zero semigroups in terms of partial chains $\Omega$ of left zero semigroups and semilattices $\Omega$ of right zero semigroups.References
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- David McLean, Idempotent semigroups, Amer. Math. Monthly 61 (1954), 110–113. MR 60505, DOI 10.2307/2307797
- R. J. Warne, Bands of maximal left groups, Rev. Roumaine Math. Pures Appl. 17 (1972), 1705–1707. MR 318366
Bibliographic Information
- © Copyright 1973 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 37 (1973), 17-21
- MSC: Primary 20M10
- DOI: https://doi.org/10.1090/S0002-9939-1973-0306380-3
- MathSciNet review: 0306380