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Characterization of the set of regular elements in ordered semigroups

In: Mathematica Slovaca, vol. 65, no. 6
Niovi Kehayopulu - Michael Tsingelis
Detaily:
Rok, strany: 2015, 1251 - 1260
Kľúčové slová:
ordered semigroup, left (right) ideal, ideal, bi-ideal, quasi-ideal, regular element, left (right) regular element, completely regular element
O článku:
We characterize the set of regular elements of an ordered semigroup $S$ which is a left (right) ideal, an ideal, a bi-ideal or a quasi-ideal of $S$ using the left (resp. right) ideal $LE(S)=\bigcupe \in E(S) (Se]$ (resp. $RE(S)=\bigcupe \in E(S) (eS]$), the ideal $IE(S)=\bigcupe \in E(S) (SeS]$, the bi-ideal $BE(S)=\bigcupe,f \in E(S) (eSf]$, and the quasi-ideal $LE(S)\cap RE(S)$ of $S$, where $E(S)$ is the set of elements of $S$ for which $e≤ e2$. Illustrative example is given.
Ako citovať:
ISO 690:
Kehayopulu, N., Tsingelis, M. 2015. Characterization of the set of regular elements in ordered semigroups. In Mathematica Slovaca, vol. 65, no.6, pp. 1251-1260. 0139-9918. DOI: https://doi.org/10.1515/ms-2015-0086

APA:
Kehayopulu, N., Tsingelis, M. (2015). Characterization of the set of regular elements in ordered semigroups. Mathematica Slovaca, 65(6), 1251-1260. 0139-9918. DOI: https://doi.org/10.1515/ms-2015-0086
O vydaní:
Publikované: 1. 12. 2015