27 research outputs found
On Shirshov bases of graded algebras
We prove that if the neutral component in a finitely-generated associative
algebra graded by a finite group has a Shirshov base, then so does the whole
algebra.Comment: 4 pages; v2: minor corrections in English; to appear in Israel J.
Mat
Algebraic Geometry over Free Metabelian Lie Algebra I: U-Algebras and Universal Classes
This paper is the first in a series of three, the aim of which is to lay the
foundations of algebraic geometry over the free metabelian Lie algebra . In
the current paper we introduce the notion of a metabelian Lie -algebra and
establish connections between metabelian Lie -algebras and special matrix
Lie algebras. We define the -localisation of a metabelian Lie
-algebra and the direct module extension of the Fitting's radical of
and show that these algebras lie in the universal closure of .Comment: 34 page