This article is cited in 1 paper

Varieties of Two-Step Solvable Algebras of Type (1,1)

S. V. Platonova

Ryazan State Pedagogical University

Abstract: The structure of the set of all non-nilpotent subvarieties of the variety of two-step solvable algebras of type (1,1) is studied. An additive basis of a free metabelian (1,1)-algebra is constructed. It is proved that any identity in a non-nilpotent metabelian (1,1)-algebra of degree $\geqslant6$ is a consequence of four defining relations.

UDC: 512.554.5

Received: 12.02.2003

DOI: 10.4213/mzm117

 English version: Mathematical Notes, 2004, 76:3, 379–388

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