NEW RESULTS ON GENERALIZATION OF JORDAN CENTRALIZERS OVER MATRIX RINGS.

This paper presents a study on Jordan maps over matrix rings with some functional equations related to additive maps on these rings. We first 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. [ABSTRACT FROM AUTHOR]