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Some Commutativity Results for S -unital Rings

Moharram A. Khan

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Abstract

In the present paper, it is shown that if R is a left ( resp. right) s-unital ring satisfying [f(ymxrys) \\pm xty, x] = 0 (resp. [f(ymxrys) \\pm yxt, x] = 0), where m, r, s, t are fixed non-negative integers and f(l) is a polynomial in {l}2{\\bf Z}[l], then R is commutative. Commutativity of R has also been investigated under different sets of constraints on integral exponents.

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What this paper is about

In the present paper, it is shown that if R is a left ( resp. right) s-unital ring satisfying [f(ymxrys) \\pm xty, x] = 0 (resp. [f(ymxrys) \\pm yxt, x] = 0), where m, r, s, t are fixed non-negative integers and f(l) is a polynomial in {l}2{\\bf Z}[l], then R is commutative. Commutativity of R has also been investigated under different sets of constraints on integral exponents.

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Available abstract

In the present paper, it is shown that if R is a left ( resp. right) s-unital ring satisfying [f(ymxrys) \\pm xty, x] = 0 (resp. [f(ymxrys) \\pm yxt, x] = 0), where m, r, s, t are fixed non-negative integers and f(l) is a polynomial in {l}2{\\bf Z}[l], then R is commutative. Commutativity of R has also been investigated under different sets of constraints on integral exponents.

Key concepts: Unital, Mathematics, Commutative property, Polynomial, Commutative ring, Polynomial ring, Ring (chemistry), Combinatorics

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