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Zapiski Nauchnykh Seminarov POMI, 2007, Volume 343, Pages 222–232
(Mi znsl117)
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This article is cited in 1 scientific paper (total in 1 paper)
$\mathcal{CS}$-indecomposable ordered semigroups
N. Kehayopulu, M. Tsingelis National and Capodistrian University of Athens, Department of Mathematics
Abstract:
An ordered semigroup $S$ is called $\mathcal{CS}$-indecomposable if the set $S\times S$ is the only complete semilattice congruence on $S$. In this paper we prove that each ordered semigroup is, uniquely, complete semilattice of $\mathcal{CS}$-indecomposable semigroups, which means that it can be decomposed into $CS$-indecomposable components in a unique way. Furthermore, the $\mathcal{CS}$-indecomposable ordered semigroups are exactly the
ordered semigroups which do not contain proper filters.
Received: 30.05.2007
Citation:
N. Kehayopulu, M. Tsingelis, “$\mathcal{CS}$-indecomposable ordered semigroups”, Problems in the theory of representations of algebras and groups. Part 15, Zap. Nauchn. Sem. POMI, 343, POMI, St. Petersburg, 2007, 222–232; J. Math. Sci. (N. Y.), 147:5 (2007), 7098–7104
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https://www.mathnet.ru/eng/znsl117 https://www.mathnet.ru/eng/znsl/v343/p222
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Abstract page: | 186 | Full-text PDF : | 59 | References: | 34 |
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