Campus Units

Mathematics

Document Type

Article

Publication Version

Published Version

Publication Date

2011

Journal or Book Title

Rocky Mountain Journal of Mathematics

Volume

41

Issue

5

First Page

1471

Last Page

1482

DOI

10.1216/RMJ-2011-41-5-1471

Abstract

A (left) centralizer for an associative ring R is an additive map satisfying T(xy) = T(x)y for all x, y in R. A (left) Jordan centralizer for an associative ring R is an additive map satisfying T(xy+yx) = T(x)y + T(y)x for all x, y in R. We characterize rings with a Jordan centralizer T. Such rings have a T invariant ideal I, T is a centralizer on R/I, and I is the union of an ascending chain of nilpotent ideals. Our work requires 2-torsion free. This result has applications to (right) centralizers, (two-sided) centralizers, and generalized derivations.

Comments

This article is published as Hentzel, Irvin R.; El-Sayiad, M.S. Tammam. "Left centralizers on rings that are not semiprime," Rocky Mountain J. Math. 41 (2011), no. 5, 1471--1482. doi:10.1216/RMJ-2011-41-5-1471. Posted with permission.

Copyright Owner

Rocky Mountain Mathematics Consortium

Language

en

File Format

application/pdf

Published Version

Included in

Algebra Commons

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