On weakly prime ideals of quasi-ordered semigroups
Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, Tome 154 (2012) no. 2, pp. 101-106
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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.
@article{UZKU_2012_154_2_a9,
author = {Yu. V. Zhuchok and L. V. Kirtadze},
title = {On weakly prime ideals of quasi-ordered semigroups},
journal = {U\v{c}\"enye zapiski Kazanskogo universiteta. Seri\^a Fiziko-matemati\v{c}eskie nauki},
pages = {101--106},
publisher = {mathdoc},
volume = {154},
number = {2},
year = {2012},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/UZKU_2012_154_2_a9/}
}
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Yu. V. Zhuchok; L. V. Kirtadze. On weakly prime ideals of quasi-ordered semigroups. Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, Tome 154 (2012) no. 2, pp. 101-106. http://geodesic.mathdoc.fr/item/UZKU_2012_154_2_a9/