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The News of Altai State University
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Mathematics and Computer Science
Mathematics and Computer Science

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A.S. Kuzmina

Varieties of algebras all subdirectly irreducible algebras of which are Armendariz

An associative algebra R is called an Armendariz algebra if for any polynomials f(x) = a0 + a1 x + … + am xm and g(x) = b0 + b1 x + … + bn xn ∈ R[x] such that f(x)g(x) = 0 we have that ai bj = 0, i = 0, 1 …, m, j = 0, 1, …, n. We describe varieties of associative algebras over a field all subdirectly irreducible algebras of which are Armendariz.

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