HIGHER LEFT DERIVATIONS ON SEMIPRIME RINGS

Park, Kyoo-Hong; Park, Kyoo-Hong

P-ISSN1226-0657
E-ISSN2287-6081
KCI

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Vol.17 No.4

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HIGHER LEFT DERIVATIONS ON SEMIPRIME RINGS

Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics / Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics, (P)1226-0657; (E)2287-6081

2010, v.17 no.4, pp.355-362

Park, Kyoo-Hong

Park,, K. (2010). HIGHER LEFT DERIVATIONS ON SEMIPRIME RINGS. Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics, 17(4), 355-362.

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Abstract

In this note, we extend the Bresar and Vukman's result [1, Proposition 1.6], which is well-known, to higher left derivations as follows: let R be a ring. (i) Under a certain condition, the existence of a nonzero higher left derivation implies that R is commutative. (ii) if R is semiprime, every higher left derivation on R is a higher derivation which maps R into its center.

keywords: higher left derivations, semiprime rings, center

Reference

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Ferrero, Miguel;Haetinger, Claus. (2002). HIGHER DERIVATIONS OF SEMIPRIME RINGS. Communications in Algebra, 30(5), 2321-2333. 10.1081/AGB-120003471.

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Article Contents

Vol.17 No.4

HIGHER LEFT DERIVATIONS ON SEMIPRIME RINGS

Abstract

Reference

Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics