Geodesic
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 Cet article a éte moissonné depuis la source Math-Net.Ru

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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. 
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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/

[1] Faith C., Algebra, v. II, Grundlehren Math. Wiss., 191, Ring theory, Springer-Verlag, Berlin–N.Y., 1976, 319 pp. | DOI | MR | Zbl

[2] Burton D. M., A First Course in Rings and Ideals, Addison-Wesley Pub. Co., Reading, Mass., 1970, 309 pp. | MR | Zbl

[3] Kehayopulu N., Ponizovskii J., Tsingelis M., “A note on maximal ideals in ordered semigroups”, Algebra Discrete Math., 2003, no. 1, 32–35 | MR | Zbl

[4] Zhuchok Yu. V., “Kvaziuporyadkovani napivgrupi ta ikh zobrazhennya”, Trudy IPMM NAN Ukrainy, 2005, no. 11, 42–48 | MR

[5] Kehayopulu N., “On weakly prime ideals of ordered semigroups”, Math. Japan, 35:6 (1990), 1051–1056 | MR | Zbl

[6] Kehayopulu N., “Weakly prime and prime fuzzy ideals in ordered semigroups”, Lobachevskii J. Math., 27 (2007), 31–40 | MR

[7] Kehayopulu N., “On prime, weakly prime ideals in ordered semigroups”, Semigroup Forum, 44:1 (1992), 341–346 | DOI | MR | Zbl

[8] Kehayopulu N., Ponizovskii J., Tsingelis M., “A note on maximal ideals in ordered semigroups”, Algebra Discrete Math., 2003, no. 1, 32–35 | MR | Zbl

[9] Shevrin L. N., “Polugruppy”, Gl. IV, Obschaya algebra, v. 2, ed. L. A. Skornyakov, Nauka, M., 1991, 11–191