NEW RESULTS ON GENERALIZATION OF JORDAN CENTRALIZERS OVER MATRIX RINGS

NEW RESULTS ON GENERALIZATION OF JORDAN CENTRALIZERS OVER MATRIX RINGS

A. Ghosh, O. Prakash, S. Singh

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Abstract

This paper presents a study on Jordan maps over matrix rings with some functional equations related to additive maps on these rings. We  rst show that every Jordan left (right) centralizer over a matrix ring is a left (right) centralizer. Moreover, every two-sided centralizer over the matrix ring is of a particular form. Further, we prove that any additive map satisfying functional equations over matrix rings becomes a two-sided centralizer. Finally, we conclude our work with some results on the Jordan left ?- centralizer over matrix rings and establish some results on functional equations that arise for the ?-centralizer.

Keywords

Prime and semiprime associative rings, Rings with involution, Jordan structure, Matrix rings, General theory of functional equations.