Varieties of linear algebras with colength one. (English. Russian original) Zbl 1304.17002
Mosc. Univ. Math. Bull. 65, No. 1, 23-27 (2010); translation from Vest. Mosk. Univ. Mat. Mekh. 65, No. 1, 25-30 (2010).
Summary: In the case of characteristic zero it is proved that there exist exactly three varieties of linear algebras with the colength equal to one for all degrees. Those are the variety of all associative-commutative algebras, the variety of all metabelian Lie algebras, and the variety of soluble Jordan algebras of the step 2 with the identity \(x^{2}x \equiv 0\).
MSC:
17A30 | Nonassociative algebras satisfying other identities |
17B01 | Identities, free Lie (super)algebras |
16R10 | \(T\)-ideals, identities, varieties of associative rings and algebras |
16R40 | Identities other than those of matrices over commutative rings |
17C05 | Identities and free Jordan structures |
References:
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