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 ≥6 is a consequence of four defining relations.
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Platonova, S.V. Varieties of Two-Step Solvable Algebras of Type (1, 1). Mathematical Notes 76, 379–388 (2004). https://doi.org/10.1023/B:MATN.0000043465.59075.88
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DOI: https://doi.org/10.1023/B:MATN.0000043465.59075.88