Journal Paper

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Journal: گستره ریاضی
Year:2012 | Volume: | Issue:
Start Page: | End Page:

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Title

A NOTE ON POWER VALUES OF DERIVATION IN PRIME AND SEMIPRIME RINGS

Pages

 Start Page 79 | End Page 88

Abstract

 Let R be a ring with DERIVATION d, such that (d (xy)) n= (d (x)) n (d (y)) n for all x, y Î R and n³1 a fixed integer. In this paper, we show that if R is prime, then d=0 or R is commutative. If R is semiprime, thend maps R into its center. Moreover in semiprime case let A=O (R) be the orthogonal completion of R and B=B (C) be the Boolian ring of C, where C is the extended centroid of R. Then there exists an idempotent e Î B such that e A is a commutative ring and d induces a zero DERIVATION on (1-e) A.

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