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Article
Left centralizers on rings that are not semiprime
Rocky Mountain Journal of Mathematics
  • Irvin R. Hentzel, Iowa State University
  • M.S. Tammam El-Sayiad
Document Type
Article
Disciplines
Publication Version
Published Version
Publication Date
1-1-2011
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
Citation Information
Irvin R. Hentzel and M.S. Tammam El-Sayiad. "Left centralizers on rings that are not semiprime" Rocky Mountain Journal of Mathematics Vol. 41 Iss. 5 (2011) p. 1471 - 1482
Available at: http://works.bepress.com/irvin-hentzel/5/