Rings over which every matrix is the sum of two idempotents and a nilpotent

2016/11/02 by Chen, H., Sheibani, M.
#FOS: Mathematics #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.1611.00525

Abstract

A ring R is (strongly) 2-nil-clean if every element in R is the sum of two idempotents and a nilpotent (that commute). Fundamental properties of such rings are discussed. Let R be a 2-primal ring. If R is strongly 2-nil-clean, we show that M_n(R) is 2-nil-clean for all n∈ \Bbb N. We also prove that the matrix ring is 2-nil-clean for a strongly 2-nil-clean ring of bounded index. These provide many classes of rings over which every matrix is the sum of two idempotents and a nilpotent.

Related

• Rings additively generated by idempotents and nilpotents
• Rings over which every matrix is the sum of a tripotent and a nilpotent
• Rings whose Non-Invertible Elements are Strongly Nil-Clean
• Rings in which every element is either a sum or a difference of a nilpotent and an idempotent
• Strong cleanness of the 2× 2 matrix ring over a general local ring