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On the commutativity of some class of rings

Published online by Cambridge University Press:  09 April 2009

Abdullah Harmanci
Affiliation:
Department of Mathematics Hacettepe University, Ankara, Turkey.
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Throughout, R will denote an associative ring with center Z. For elements x, y of R and k a positive integer, we define inductively [x, y]0 = x, [x, y] = [x, y]1 = xyyx, [x, y, y, hellip, y]k = [[x, y, y, hellip, y]k−1, y]. A ring R is said to satisfy the k-th Engel condition if [x, y, y, hellip, y]k = 0. By an integral domain we mean a nonzero ring without nontrivial zero divisors.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 1976

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