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- Title
On the Varieties of Commutative Metabelian Algebras.
- Authors
Mishchenko, S. P.; Panov, N. P.; Frolova, Yu. Yu.; Nguyen, Trang
- Abstract
The paper presents new results on varieties of commutative metabelian algebras over a field of zero characteristic. We study the structure of the multilinear part of the variety of all commutative metabelian algebras as a module of the symmetric group. Two almost nilpotent varieties are introduced and studied in this class of algebras. We prove the nonexistence of other almost nilpotent commutative metabelian varieties of subexponential growth.
- Subjects
COMMUTATIVE algebra; ABELIAN groups; BILINEAR forms; LINEAR algebra; POLYNOMIALS
- Publication
Journal of Mathematical Sciences, 2018, Vol 233, Issue 5, p713
- ISSN
1072-3374
- Publication type
Article
- DOI
10.1007/s10958-018-3959-x