Remarks on Jordan derivations over matrix algebras

TL;DR

This paper proves that all Jordan derivations on upper triangular and full matrix algebras over a commutative ring are inner derivations, extending known results in algebra.

Contribution

It establishes that Jordan derivations on these matrix algebras are necessarily inner, generalizing previous findings to broader algebraic structures.

Findings

Jordan derivations on T_n(C) are inner

Jordan derivations on M_n(C) are inner

Extension of results to matrix algebras over commutative rings

Abstract

Let C be a commutative ring with unity. In this article, we show that every Jordan derivation over an upper triangular matrix algebra T_n(C) is an inner derivation. Further, we extend the result for Jordan derivation on full matrix algebra M_n(C).