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Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2008, Number 12, Pages 28–33
(Mi ivm1465)
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This article is cited in 1 scientific paper (total in 1 paper)
Ordered semigroups having the $P$-property
N. Kehayopulu, M. Tsingelis University of Athens, Athens, Greece
Abstract:
The main results of the paper are the following. The ordered semigroups which have the $P$-property are decomposable into archimedean semigroups. Moreover, the ordered semigroups which have the $P$-property are decomposable into semigroups having the $P$-property. Conversely, if an ordered semigroup $S$ is a complete semilattice of semigroups which have the $P$-property, then $S$ itself has the $P$-property as well. An ordered semigroup is $CS$-indecomposable and has the $P$-property if and only if it is archimedean. If $S$ is an ordered semigroup, then the relation $N:=\{(a,b)\mid N(a)=N(b)\}$ (where $N(a)$ is the filter of $S$ generated by $a$ $(a\in S)$) is the least complete semilattice congruence on $S$ and the class $(a)_{N}$ is $CS$-indecomposable subsemigroup of $S$ for every $a\in S$. The concept of the $P_m$-property is introduced and a characterization of the $P_m$-property in terms of the $P$-property is given. Our methodology simplifies the proofs of the corresponding results of semigroups (without order)
Keywords:
archimedean ordered semigroup, $P$-property, complete semilattice of semigroups of type $ T$, ideal, filter, $CS$-indecomposable ordered semigroup, $P_m$-property.
Received: 23.11.2006
Citation:
N. Kehayopulu, M. Tsingelis, “Ordered semigroups having the $P$-property”, Izv. Vyssh. Uchebn. Zaved. Mat., 2008, no. 12, 28–33; Russian Math. (Iz. VUZ), 52:12 (2008), 23–27
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https://www.mathnet.ru/eng/ivm1465 https://www.mathnet.ru/eng/ivm/y2008/i12/p28
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Abstract page: | 270 | Full-text PDF : | 67 | References: | 34 | First page: | 3 |
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