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

2017/02/18 by Marjan Sheibani, H Chen, Sheibani, M +1
Computer Science · Mathematics · #Advanced Algebra and Logic #Advanced Topics in Algebra #FOS: Mathematics #Rings and Algebras (math.RA) #Rings, Modules, and Algebras

paper · pdf · doi:10.48550/arxiv.1702.05605

openalex publication_date 2017/02/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

A ring R is trinil clean if every element in R is the sum of a tripotent and a nilpotent. If R is a 2-primal strongly 2-nil-clean ring, we prove that M_n(R) is trinil clean for all n∈ \Bbb N. Furthermore, we show that the matrix ring over a strongly 2-nil-clean ring of bounded index is trinil clean. We thereby provide various type of rings over which every matrix is the sum of a tripotent and a nilpotent.

Citations

• Nil clean rings

Related

• Rings over which every matrix is the sum of two idempotents and a nilpotent
• Matrices over Zhou nil-clean rings
• Rings in which every element is either a sum or a difference of a nilpotent and an idempotent
• Rings whose Non-Invertible Elements are Strongly Nil-Clean
• Nil-clean matrix rings