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 $\Omega$-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 $\Omega$-algebras over an infinite field (in particular, over a field of characteristic zero). These algebras include, in particular, nonassociative algebras.
Bibliography: 25 titles.
This publication is cited in the following 4 articles:
A. V. Mikhalev, “Algebras with single defining relation”, J. Math. Sci., 283:6 (2024), 919–928
V. A. Artamonov, A. V. Klimakov, A. A. Mikhalev, A. V. Mikhalev, “Primitive and almost primitive elements of Schreier varieties”, J. Math. Sci., 237:2 (2019), 157–179
Pure and Applied Mathematics, 84, Polynomial Identities in Ring Theory, 1980, 341
T. M. Baranovich, M. S. Burgin, “Linear $\Omega$-algebras”, Russian Math. Surveys, 30:4 (1975), 65–113
Citation in format AMSBIB
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