Multiplicativity of left centralizers forcing additivity

Mohammad Sayed Tammam El-Sayiad; Mohamad Nagy Daif; Vincenzo De Filippis

doi:10.5269/bspm.v32i1.17274

Mohammad Sayed Tammam El-Sayiad King Abdulaziz University Faculty of Science for Girls Department of Mathematics
Mohamad Nagy Daif Al-Azhar University Faculty of Science Departmento of Mathematics
Vincenzo De Filippis University of Messina Department of Mathematics and Computer Sciences

DOI: https://doi.org/10.5269/bspm.v32i1.17274

Keywords: Prime rings, Semiprime Rings, Centralizers, Pierce decomposition

Abstract

A multiplicative left centralizer for an associative ring R is a map satisfying T(xy) = T\(x)y for all x,y in R. T is not assumed to be additive. In this paper we deal with the additivity of the multiplicative left centralizers in a ring which contains an idempotent element. Specially, we study additivity for multiplicative left centralizers in prime and semiprime rings which contain an idempotent element.

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