Представление матриц над полями в виде матриц с нулевым квадратом и диагональных матриц П. Данчев Пётр Данчев -доктор математики, Институт математики и информатики Болгарской академии наук (г. София, Болгария).

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.

MSC2020: 16U99, 16E50, 13B99 © P. V. Danchev WEAKLY INVO-CLEAN RINGS HAVING WEAK INVOLUTIONWe completely describe up to an isomorphism the structure of weakly invo-clean rings possessing weak involution. The obtained results expand two own establishments, namely those from Afrika Mat. ( 2017) concerning weakly invo-clean rings as well as those from Far East J. Math. Sci. ( 2021) concerning invo-clean rings with weak involution.