Geodesic
Commutativity of rings with polynomial constraints
Czechoslovak Mathematical Journal, Tome 52 (2002) no. 2, pp. 401-413 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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Let $p$, $ q$ and $r$ be fixed non-negative integers. In this note, it is shown that if $R$ is left (right) $s$-unital ring satisfying $[f(x^py^q) - x^ry, x] = 0$ ($[f(x^py^q) - yx^r, x] = 0$, respectively) where $f(\lambda ) \in {\lambda }^2{\mathbb Z}[\lambda ]$, then $R$ is commutative. Moreover, commutativity of $R$ is also obtained under different sets of constraints on integral exponents. Also, we provide some counterexamples which show that the hypotheses are not altogether superfluous. Thus, many well-known commutativity theorems become corollaries of our results.
Let $p$, $ q$ and $r$ be fixed non-negative integers. In this note, it is shown that if $R$ is left (right) $s$-unital ring satisfying $[f(x^py^q) - x^ry, x] = 0$ ($[f(x^py^q) - yx^r, x] = 0$, respectively) where $f(\lambda ) \in {\lambda }^2{\mathbb Z}[\lambda ]$, then $R$ is commutative. Moreover, commutativity of $R$ is also obtained under different sets of constraints on integral exponents. Also, we provide some counterexamples which show that the hypotheses are not altogether superfluous. Thus, many well-known commutativity theorems become corollaries of our results.
Classification : 16R50, 16U70, 16U80, 16U99
Keywords: automorphism; commutativity; local ring; polynomial identity; $s$-unital ring 
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}
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Khan, Moharram A. Commutativity of rings with polynomial constraints. Czechoslovak Mathematical Journal, Tome 52 (2002) no. 2, pp. 401-413. http://geodesic.mathdoc.fr/item/CMJ_2002_52_2_a15/

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