Geodesic
On the join of Cross varieties of algebras
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 18 (2021) no. 2, pp. 1299-1306

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We constructed the example of the join Cross varieties of algebras over a finite field which is not finitely based, but its proper subvarieties is finitely based.
Keywords: linear algebra, Cross variety, nonfinitely based variety of algebras. 
I. M. Isaev. On the join of Cross varieties of algebras. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 18 (2021) no. 2, pp. 1299-1306. http://geodesic.mathdoc.fr/item/SEMR_2021_18_2_a9/
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[1] S. Oates, M.B. Powell, “Identical relations in finite groups”, J. Algebra, 1:1 (1964), 11–39 | DOI | Zbl

[2] I.V. L'vov, “Varieties of associative rings, I”, Algebra Logik, 12:3 (1974), 150–167 | DOI | Zbl

[3] I.V. L'vov, “Varieties of associative rings, II”, Algebra Logik, 12:6 (1975), 381–393 | DOI | Zbl

[4] I.V. L'vov, “Varieties generated by finite alternative rings”, Algebra Logik, 17:3 (1979), 195–198 | DOI | Zbl

[5] R.L. Kruse, “Identities satisfied by a finite rings”, J. Algebra, 26:2 (1973), 298–318 | DOI | Zbl

[6] S.V. Polin, “About identities of finite algebras”, Sib. Math. J., 17:6 (1976), 1356–1366 | Zbl

[7] I.V. L'vov, “Finite dimensional algebras with infinite bases of identities”, Sib. Math. J., 19:1 (1978), 91–99 | Zbl

[8] Yu.A. Medvedev, “Cross varieties of algebras”, Math. USSR, Sb., 43:3 (1982), 347–376 | DOI | Zbl

[9] S.O. MacDonald, M.R. Vaughan-Lee, “Varieties that make one Cross”, J. Aust. Math. Soc., Ser. A, 26:3 (1978), 368–382 | DOI | Zbl

[10] I.M. Isaev, “Finite-dimensional right alternative algebras that do not generate finitely based varieties”, Algebra Logik, 25:2 (1986), 86–96 | DOI | Zbl

[11] I.M. Isaev, “Essentially infinitely based varieties of algebras”, Sib. Math. J., 30:6 (1989), 892–894 | DOI | Zbl

[12] I.M. Isaev, “Finite algebras with no independent basis of identities”, Algebra Univers., 37:4 (1997), 440–444 | DOI | Zbl

[13] K.A. Baker, “Finite equational bases for finite algebras in a congruence-distributive equational class”, Adv. Math., 24:3 (1977), 207–243 | DOI | Zbl

[14] I.M. Isaev, “On the join of Spechtian varieties of algebras”, Sib. Électron. Math. Izv., 15 (2018), 1498–1505 | DOI | Zbl

[15] Yu.N. Mal'tsev, E.N. Kuz'min, “A basis for the identities of the algebra of second-order matrices over a finite field”, Algebra Logik, 17:1 (1978), 18–21 | DOI | Zbl