Scientific journal "The News of Altai State University". 2004 #1(31). Mathematics and Computer Science.

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2004

$Mathematics and Computer Science$

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E.V. Zhuravlev

Some conditions commutativity of rings

The author obtained following result:

Theorem. Let R # be a associative ring such that for each a, b ∈ R there exists k ∈ N and polynomials f(x), g(x) ∈ {x # x²p(x); p(x) ∈ Z[x]} such that [f(f), g(b)] = [f(f), g(b)]_k. Then R # is a commutative in each of the following cases:

1. char(R) ≠ 0, N(R) = 0 and k = k(a, b);

2. char(R) = 0, f(x), g(x) # are fixed polynomials and k = k(b).

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