FAR EASTERN BRANCH OF THE RUSSIAN ACADEMY OF SCIENCES
INSTITUTE OF APPLIED MATHEMATICS KHABAROVSK DIVISION
Far Eastern Mathematical Journal
Modularity conditions of the lattice of congruences of acts over right or left zero semigroups |
Khaliullina A. R. |
2015, issue 1, P. 102-120 |
Abstract |
| We obtain necessary and sufficient conditions for modularity and distributivity of the lattice of congruences of acts over right or left zeros semigroup, as well as the conditions under which the congruence lattice is a chain. We describe the congruences of arbitrary act over left zero semigroup. |
Keywords: congruences, act, semigroup |
Download the article (PDF-file) |
References |
| [1] G. Gretcer, Obshhaja teorija reshjotok, Mir, M., 1982. [2] A. A. Tuganbaev, “Stroenie distributivnyh kolec”, Mat. sbornik, 193:5 (2002), 113–128. [3] A. A. Tuganbaev, Teorija kolec. Arifmeticheskie moduli i kol'ca, MCNMO, M., 2009. [4] D. P. Egorova, “Struktura kongrujencij unarnoj alegbry”, Mezhvuz. nauchn. sb. ""Uporjadochennye mnozhestva i reshjotki"". T. 5, Saratov, 1978, 11–44. [5] I. B. Kozhukhov, ""Left chain semigroups"", Semigroup Forum, 222:1 (1981), 1-8. [6] D. O. Ptahov, A. A. Stepanova, “Reshjotki kongrujencij poligonov”, Dal'nevost. matemem. zhurnal, 13:1 (2013), 107–115. [7] A. Klifford, G. Preston, Algebraicheskaja teorija polugrupp. T. 1, Mir, M., 1972. [8] A. Klifford, G. Preston, Algebraicheskaja teorija polugrupp. T. 2, Mir, M., 1974. [9] M. Kilp, U. Knauer, A. V. Mikhalev, Monoids, acts and categories, W. de Gruyter, N.Y.-Berlin, 2000. [10] A.Yu. Avdeyev, I. B. Kozhukhov, ""Acts over completely 0-simple semigroups"", Acta Cybernetica, 14:4 (2000), 523-531. [11] A.R. Haliullina, “Kongrujencii poligonov nad polugruppami pravyh nulej”, Che-bysh. sbornik, 14:3 (2013), 142–146. |