On the idempotent and nilpotent sum numbers of matrices over certain indecomposable rings and related concepts

Abstract

We investigate a few special decompositions in arbitrary rings and matrix rings over indecomposable rings into nilpotent and idempotent elements. Moreover, we also define and study the nilpotent sum trace number of nilpotent matrices over an arbitrary ring. Some related notions are explored as well.

Keywords

• idempotents; nilpotents; commutators; traces; matrices.