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Semigroup actions on ordered groupoids

In: Mathematica Slovaca, vol. 63, no. 1
Niovi Kehayopulu - Michael Tsingelis
Detaily:
Rok, strany: 2013, 41 - 52
Kľúčové slová:
semigroup, ordered groupoid, action, embedding, cancellative ordered groupoid, quasi-order
O článku:
In this paper we prove that if $S$ is a commutative semigroup acting on an ordered groupoid $G$, then there exists a commutative semigroup $\widetilde S$ acting on the ordered groupoid $\widetilde G:=(G× S)/\overlineρ$ in such a way that $G$ is embedded in $\widetilde G$. Moreover, we prove that if a commutative semigroup $S$ acts on an ordered groupoid $G$, and a commutative semigroup $\overline S$ acts on an ordered groupoid $\overline G$ in such a way that $G$ is embedded in $\overline G$, then the ordered groupoid $\widetilde G$ can be also embedded in $\overline G$. We denote by $\overlineρ$ the equivalence relation on $G× S$ which is the intersection of the quasi-order $ρ$ (on $G× S$) and its inverse $ρ-1$.
Ako citovať:
ISO 690:
Kehayopulu, N., Tsingelis, M. 2013. Semigroup actions on ordered groupoids. In Mathematica Slovaca, vol. 63, no.1, pp. 41-52. 0139-9918. DOI: https://doi.org/10.2478/s12175-012-0080-3

APA:
Kehayopulu, N., Tsingelis, M. (2013). Semigroup actions on ordered groupoids. Mathematica Slovaca, 63(1), 41-52. 0139-9918. DOI: https://doi.org/10.2478/s12175-012-0080-3
O vydaní:
Publikované: 1. 2. 2013