On quasi-prime, weakly quasi-prime left ideals in ordered-$Γ$-semigroups

In: Mathematica Slovaca, vol. 60, no. 2

Kostaq Hila

Detaily:

Rok, strany: 2010, 195 - 212

Kľúčové slová:

$\Gamma$-semigroup, ordered $\Gamma$-semigroups (po-$\Gamma$-semigroup), left ideal, quasi-prime, weakly quasi-prime, $m$-system, weak $m$-system, semiprime, strongly semiprime

DOI: https://doi.org/10.2478/s12175-010-0006-x

O článku:

In this paper we obtain and establish some important results in ordered $Γ$-semigroups extending and generalizing those for semigroups given in [PETRICH, M.:\textit{Introduction to Semigroups}, Merill, Columbus, 1973] and for ordered semigroups from [KEHAYOPULU, N.:\textit{On weakly prime ideals of ordered semigroups}, Math. Japon. \textbf{35} (1990), 1051–1056], [KEHAYOPULU, N.:\textit{On prime, weakly prime ideals in ordered semigroups}, Semigroup Forum \textbf{44} (1992), 341–346] and [XIE, X. Y.—WU, M. F.: \textit{On quasi-prime, weakly quasi-prime left ideals in ordered semigroups}, PU.M.A. \textbf{6} (1995), 105–120]. We introduce and give some characterizations about the quasi-prime and weakly quasi-prime left ideals of ordered-$Γ$-semigroups. We also introduce the concept of weakly $m$-systems in ordered $Γ$-semigroups and give some characterizations of the quasi-prime and weakly quasi-prime left ideals by weakly $m$-systems.

Ako citovať:

ISO 690:

Hila, K. 2010. On quasi-prime, weakly quasi-prime left ideals in ordered-$Γ$-semigroups. In Mathematica Slovaca, vol. 60, no.2, pp. 195-212. 0139-9918. DOI: https://doi.org/10.2478/s12175-010-0006-x

APA:

Hila, K. (2010). On quasi-prime, weakly quasi-prime left ideals in ordered-$Γ$-semigroups. Mathematica Slovaca, 60(2), 195-212. 0139-9918. DOI: https://doi.org/10.2478/s12175-010-0006-x

O vydaní: