On weakly prime ideals of quasi-ordered semigroups

Yu. V. Zhuchok^a, L. V. Kirtadze<sup>b

a</sup> Lugansk Taras Shevchenko National University, Lugansk, Ukraine
^b Abkhazian State University, Sukhumi, Abkhazia

Abstract: We prove that every maximal ideal of a cone quasi-ordered semigroup is a weakly prime ideal. We found necessary and sufficient conditions under which all ideals of a quasi-ordered semigroup are weakly prime.

Keywords: quasi-ordered semigroup, weakly $n$-prime subset, weakly prime ideal, maximal ideal.

UDC: 512.53

Received: 28.12.2011