SCHREIER VARIETIES OF LINEAR Ω-ALGEBRAS

Abstract

A variety of universal algebras is called a Schreier variety if every subalgebra of any free algebra in that variety is also free in that variety. This paper gives a description of the Schreier varieties of linear Ω-algebras over an associative commutative ring, defined by systems of homogeneous identities. As a corollary to these results one obtains a description of all Schreier varieties of linear Ω-algebras over an infinite field (in particular, over a field of characteristic zero). These algebras include, in particular, nonassociative algebras. Bibliography: 25 items.