ON COMMUTATIVITY OF ONE-SIDED $s$-UNITAL RINGS
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Abstract
In the present paper, we study the commutativity of one sided s-unital rings satisfying conditions of the form $[x^r y\pm x^ny^mx^s,x]= 0 = [x^ry^m\pm x^ny^{m^2}x^s, x]$, or $[yx^r\pm x^ny^mx^s, x] = 0 = [y^mx^r\pm x^ny^{m^2}x^s, x]$ for each $x$,$y \in R$, where $m = m(y) > 1$ is an integer depending on $y$ and $n$, $r$ and $s$ are fixed non-negative integers. Other commutativity theorems are also obtained. Our results generalize·some of the well-known commutativity theorems for rings.
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