Geodesic
On $\omega$-independent bases for quasi-identities
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 14 (2017), pp. 838-847.

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

In this article, we continue the study of complexity of quasivariety lattices. We prove that there are continuum many quasivarieties of graphs, monounary algebras, digraphs, and pointed Abelian groups having an $\omega$-independet quasi-equational basis.
Keywords: quasivariety, quasi-equational basis, $\omega$-independent basis. 
@article{SEMR_2017_14_a22,
     author = {A. Basheyeva and A. V. Yakovlev},
     title = {On $\omega$-independent bases for quasi-identities},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {838--847},
     publisher = {mathdoc},
     volume = {14},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2017_14_a22/}
}
TY  - JOUR
AU  - A. Basheyeva
AU  - A. V. Yakovlev
TI  - On $\omega$-independent bases for quasi-identities
JO  - Sibirskie èlektronnye matematičeskie izvestiâ
PY  - 2017
SP  - 838
EP  - 847
VL  - 14
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SEMR_2017_14_a22/
LA  - ru
ID  - SEMR_2017_14_a22
ER  - 
%0 Journal Article
%A A. Basheyeva
%A A. V. Yakovlev
%T On $\omega$-independent bases for quasi-identities
%J Sibirskie èlektronnye matematičeskie izvestiâ
%D 2017
%P 838-847
%V 14
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SEMR_2017_14_a22/
%G ru
%F SEMR_2017_14_a22
A. Basheyeva; A. V. Yakovlev. On $\omega$-independent bases for quasi-identities. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 14 (2017), pp. 838-847. http://geodesic.mathdoc.fr/item/SEMR_2017_14_a22/

[1] V. A. Gorbunov, “Coverings in lattices of quasivarieties and independent axiomatizability”, Algebra and Logic, 16:5 (1977), 507–548 | DOI | MR | Zbl

[2] V. A. Gorbunov, Algebraic Theory of Quasivarieties, Plenum, New York, 1998 | MR

[3] A. I. Maltsev, “Universally axiomatizable subclasses of locally finite classes of models”, Siberian Math. J., 8:5 (1967), 1005–1014 | MR | Zbl

[4] A. I. Budkin, “Independent axiomatizability of quasivarieties of groups”, Mathematical Notes, 31:6 (1982), 817–826 | DOI | MR | Zbl

[5] A. I. Budkin, “Independent axiomatizability of quasivarieties of generalized solvable groups”, Algebra i Logika, 25:3 (1986), 249–266 | DOI | MR | Zbl

[6] A. I. Budkin, “Independent axiomatizability of quasivarieties of generalized solvable groups”, Algebra and Logic, 30:2 (1991), 125–153 | DOI | MR | Zbl

[7] N. Ya. Medvedev, “On quasivariety of $l$-groups and groups”, Siberian Math. J., 26:5 (1985), 111–117 | MR | Zbl

[8] V. K. Kartashov, “Quasivarieties of unars”, Mathematical Notes, 27:1 (1980), 5–12 | DOI | MR | Zbl

[9] A. V. Kartashova, “Antivarieties of unars”, Algebra and Logic, 50:4 (2011), 357–364 | DOI | MR | Zbl

[10] A. V. Kravchenko, “On the lattice complexity of quasivarieties of graphs and endographs”, Algebra and Logic, 36:3 (1997), 164–168 | DOI | MR | Zbl

[11] A. V. Kravchenko, “$\mathcal{Q}$-universal quasivarieties of graphs”, Algebra and Logic, 41:3 (2002), 173–181 | DOI | MR | Zbl

[12] A. V. Kravchenko, “On the complexity of quasivariety lattices for varieties of unary algebras. II”, Siberian Electronic Math. Reports, 13 (2016), 388–394 | MR | Zbl

[13] A. V. Kravchenko, A. V. Yakovlev, Quasivarieties of graphs and independent axiomatizability, submitted for publication in 2017

[14] S. V. Sizyi, “Quasivarieties of graphs”, Siberian Math. J., 35 (1994), 783–794 | DOI | MR

[15] V. I. Tumanov, “Finite lattices having no independent basis of quasi-identities”, Mathematical Notes, 36:5 (1984), 811–815 | DOI | MR | Zbl

[16] A. N. Fedorov, “Quasi-identities of a free 2-nilpotent group”, Mathematical Notes, 40:5 (1986), 590–597 | DOI | MR | Zbl

[17] A. Basheyeva, A. M. Nurakunov, M. V. Schwidefsky, A. Zamojska-Dzienio, “Lattices of subclasses. III”, Siberian Electronic Math. Reports, 14 (2017), 252–263 | MR | Zbl

[18] Z. Hedrlín, A. Pultr, “Symmetric relations $($undirected graphs$)$ with given semigroups”, Monatsch. Math., 69:4 (1965), 318–324 | DOI | MR

[19] A. V. Kravchenko, A. M. Nurakunov, M. V. Schwidefsky, On quasi-equational bases of differential groupoids and unary algebras, submitted for publication in 2017

[20] A. Tarski, “Equational logic and equational theories of algebras”, Contrib. Math. Logic, 8 (1966), 275–288 | MR