Scientific journal "The News of Altai State University". 2007 #1(53). Mathematics and Computer Science.

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2007

$Mathematics and Computer Science$

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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 + … + a_m x^m and g(x) = b₀ + b₁ x + … + b_n xⁿ ∈ R[x] such that f(x)g(x) = 0 we have that a_i b_j = 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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