Geodesic
The strongly faithful $S$-acts over commutative monoids and groups with modular congruence lattices
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 13 (2016), pp. 1067-1077.

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

In this article we describe the strongly faithful $S$-acts over commutative monoids and groups with distributive, modular and linear congruence lattices.
Keywords: lattice, modular lattice, distributive lattice, linear lattice, congruence lattice of algebra, $S$-act, strongly faithful $S$-act. 
@article{SEMR_2016_13_a33,
     author = {A. A. Stepanova and N. V. Trikashnaya},
     title = {The strongly faithful $S$-acts over commutative monoids and groups with modular congruence lattices},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {1067--1077},
     publisher = {mathdoc},
     volume = {13},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2016_13_a33/}
}
TY  - JOUR
AU  - A. A. Stepanova
AU  - N. V. Trikashnaya
TI  - The strongly faithful $S$-acts over commutative monoids and groups with modular congruence lattices
JO  - Sibirskie èlektronnye matematičeskie izvestiâ
PY  - 2016
SP  - 1067
EP  - 1077
VL  - 13
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SEMR_2016_13_a33/
LA  - ru
ID  - SEMR_2016_13_a33
ER  - 
%0 Journal Article
%A A. A. Stepanova
%A N. V. Trikashnaya
%T The strongly faithful $S$-acts over commutative monoids and groups with modular congruence lattices
%J Sibirskie èlektronnye matematičeskie izvestiâ
%D 2016
%P 1067-1077
%V 13
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SEMR_2016_13_a33/
%G ru
%F SEMR_2016_13_a33
A. A. Stepanova; N. V. Trikashnaya. The strongly faithful $S$-acts over commutative monoids and groups with modular congruence lattices. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 13 (2016), pp. 1067-1077. http://geodesic.mathdoc.fr/item/SEMR_2016_13_a33/

[1] D. P. Egorova, L. A. Skornyakov, “About the structure of the congruence of the unary algebra”, Mejvuzovskii nauchnii sbornik, Uporyadochennie mnojestva i reshetki, 1977, 28–40 | MR | Zbl

[2] D. P. Egorova, “The structure of the congruence of the unary algebra”, Mejvuzovskii nauchnii sbornik, Uporyadochennie mnojestva i reshetki, 5, 1978, 11–44 | MR | Zbl

[3] D. O. Ptakhov, A. A. Stepanova, “Congruence's lattice of the polygon”, Dal'nevostochnyj matematicheskij zhurnal, 13:1 (2013), 107–116 | MR | Zbl

[4] A. R. Khaliullina, “Terms of modularity of the lattice congruence polygon over the semigroup of left and right zeroes”, Dal'nevostochnyj matematicheskij zhurnal, 15:1 (2015), 102–120 | Zbl

[5] M. Kilp, U. Knauer, A. V. Mikhalev, Monoids, Acts, and Categories, Walter de Gruyter, Berlin, 2000 | MR | Zbl

[6] L. A. Skornyakov, Elements of general algebra, Nauka, M., 1983 | MR | Zbl

[7] M. Suzuki, Structure of a Group and the Structure of its Lattice of Subgroups, Erg. Math., 10, Springer, Berlin, 1956 | MR | Zbl

[8] B. Pondelicek, “Modularity and distributivity of tolerance lattices of commutative separative semigroups”, Czechoslovak Mathematical Journal, 35:2 (1985), 333–337 | MR | Zbl

[9] H. Mitsch, “Semigroups and their lattice of Coungruence II”, Semigroup forum, 54 (1997), 1–42 | DOI | MR | Zbl

[10] L. A. Skornyakov, Elements of the theory of structures, Nauka, M., 1982 | MR | Zbl

[11] A. H. Clifford, G. B. Preston, The algebraic theory of semigroups, Math. Surveys, 7, Amer. Math. Soc., Providence, R.I., 1961 | MR | Zbl

[12] A. G. Kurosh, The theory of groups, Nauka, M., 1967 | MR | Zbl

[13] M. Hall, Jr., The theory of groups, MacMillan Co., New York, 1959 | MR | Zbl

[14] G. Gretzer, General theory of structures, Mir, M., 1981