Multiplicativity of left centralizers forcing additivity

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.

Keywords

• Prime rings
• Semiprime Rings
• Centralizers
• Pierce decomposition