On $\omega$-independent bases for quasi-identities
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 14 (2017), pp. 838-847 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

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},
     year = {2017},
     volume = {14},
     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
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
%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