In: Mathematica Slovaca, vol. 63, no. 3
Niovi Kehayopulu - Michael Tsingelis
Detaily:
Rok, strany: 2013, 411 - 416
Kľúčové slová:
semigroup, ordered semigroup, left simple, left (right) regular, intra-regular, left (right) ideal, ideal, semilattice (complete semilattice) congruence, semilattice (complete semilattice) of left simple semigroups
O článku:
It has been proved by Tôru Saitô that a semigroup $S$ is a semilattice of left simple semigroups, that is, it is decomposable into left simple semigroups, if and only if the set of left ideals of $S$ is a semilattice under the multiplication of subsets, and that this is equivalent to say that $S$ is left regular and every left ideal of $S$ is two-sided. Besides, S. Lajos has proved that a semigroup $S$ is left regular and the left ideals of $S$ are two-sided if and only if for any two left ideals $L_1$, $L_2$ of $S$, we have $L_1\cap L_2=L_1L_2$. The present paper generalizes these results in case of ordered semigroups. Some additional information concerning the semigroups (without order) are also obtained.
Ako citovať:
ISO 690:
Kehayopulu, N., Tsingelis, M. 2013. On ordered semigroups which are semilattices of left simple semigroups. In Mathematica Slovaca, vol. 63, no.3, pp. 411-416. 0139-9918. DOI: https://doi.org/10.2478/s12175-013-0105-6
APA:
Kehayopulu, N., Tsingelis, M. (2013). On ordered semigroups which are semilattices of left simple semigroups. Mathematica Slovaca, 63(3), 411-416. 0139-9918. DOI: https://doi.org/10.2478/s12175-013-0105-6
O vydaní: