NILPOTENT AND LINEAR COMBINATION OF IDEMPOTENT MATRICES

Authors : Marjan Sheibani ABDOLYOUSEFI

Pages : 220-228

Doi:10.24330/ieja.768269

View : 14 | Download : 10

Publication Date : 2020-07-14

Article Type : Research Paper

Abstract :A ring $R$ is Zhou nil-clean if every element in $R$ is the sum of a nilpotent and two tripotents. Let $R$ be a Zhou nil-clean ring. If $R$ is of bounded index or 2-primal, we prove that every square matrix over $R$ is the sum of a nilpotent and a linear combination of two idempotents. This provides a large class of rings over which every square matrix has such decompositions by nilpotent and linear combination of idempotent matrices. $~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~$
Keywords : Idempotent matrix, nilpotent matrix, linear combination, Zhou nil clean ring