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A commutativity theorem for power-associative rings
Published online by Cambridge University Press: 17 April 2009
Abstract
Let R be a power-associative ring with identity and let I be an ideal of R such that R/I is a finite field and x ≡ y (mod I) implies x2 = y2 or both x and y commute with all elements of I. It is proven that R must then be commutative. Examples are given to show that R need not be commutative if various parts of the hypothesis are dropped or if “x2 = y2” is replaced by “xk = yk” for any integer k > 2.
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- Copyright © Australian Mathematical Society 1970
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