Geodesic
Modularity conditions of the lattice of congruences of acts over right or left zero semigroups
Dalʹnevostočnyj matematičeskij žurnal, Tome 15 (2015) no. 1, pp. 102-120 
A. R. Khaliullina. Modularity conditions of the lattice of congruences of acts over right or left zero semigroups. Dalʹnevostočnyj matematičeskij žurnal, Tome 15 (2015) no. 1, pp. 102-120. http://geodesic.mathdoc.fr/item/DVMG_2015_15_1_a9/
@article{DVMG_2015_15_1_a9,
     author = {A. R. Khaliullina},
     title = {Modularity conditions of the lattice of congruences of acts over right or left zero semigroups},
     journal = {Dalʹnevosto\v{c}nyj matemati\v{c}eskij \v{z}urnal},
     pages = {102--120},
     year = {2015},
     volume = {15},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DVMG_2015_15_1_a9/}
}
TY  - JOUR
AU  - A. R. Khaliullina
TI  - Modularity conditions of the lattice of congruences of acts over right or left zero semigroups
JO  - Dalʹnevostočnyj matematičeskij žurnal
PY  - 2015
SP  - 102
EP  - 120
VL  - 15
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/DVMG_2015_15_1_a9/
LA  - ru
ID  - DVMG_2015_15_1_a9
ER  - 
%0 Journal Article
%A A. R. Khaliullina
%T Modularity conditions of the lattice of congruences of acts over right or left zero semigroups
%J Dalʹnevostočnyj matematičeskij žurnal
%D 2015
%P 102-120
%V 15
%N 1
%U http://geodesic.mathdoc.fr/item/DVMG_2015_15_1_a9/
%G ru
%F DVMG_2015_15_1_a9

Voir la notice de l'article provenant de la source Math-Net.Ru

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.

[1] G. Grettser, Obschaya teoriya reshetok, Mir, M., 1982 | MR

[2] A. A. Tuganbaev, “Stroenie distributivnykh kolets”, Mat. sbornik, 193:5 (2002), 113–128 | DOI | MR | Zbl

[3] A. A. Tuganbaev, Teoriya kolets. Arifmeticheskie moduli i koltsa, MTsNMO, M., 2009

[4] D. P. Egorova, “Struktura kongruentsii unarnoi alegbry”, Mezhvuz. nauchn. sb. “Uporyadochennye mnozhestva i reshetki”, v. 5, Saratov, 1978, 11–44 | MR | Zbl

[5] I. B. Kozhukhov, “Left chain semigroups”, Semigroup Forum, 222:1 (1981), 1–8 | DOI | MR

[6] D. O. Ptakhov, A. A. Stepanova, “Reshetki kongruentsii poligonov”, Dalnevost. matemem. zhurnal, 13:1 (2013), 107–115 | MR | Zbl

[7] A. Klifford, G. Preston, Algebraicheskaya teoriya polugrupp, v. 1, Mir, M., 1972

[8] A. Klifford, G. Preston, Algebraicheskaya teoriya polugrupp, v. 2, Mir, M., 1974

[9] M. Kilp, U. Knauer, A. V. Mikhalev, Monoids, acts and categories, W. de Gruyter, N.Y.–Berlin, 2000 | MR | Zbl

[10] A. Yu. Avdeyev, I. B. Kozhukhov, “Acts over completely 0-simple semigroups”, Acta Cybernetica, 14:4 (2000), 523–531 | MR | Zbl

[11] A. R. Khaliullina, “Kongruentsii poligonov nad polugruppami pravykh nulei”, Chebysh. sbornik, 14:3 (2013), 142–146