Nil Clean Ideal

2017/09/07 by Ajay K‎. ‎Sharma, Dhiren Kumar Basnet, Sharma, Ajay +1
Engineering · #16N40 #16U99 #FOS: Mathematics #Physics and Engineering Research Articles #Rings and Algebras (math.RA)

paper · pdf · doi:10.48550/arxiv.1709.02065

openalex publication_date 2017/09/07 · openalex created_date 2024/04/11 · openalex updated_date 2026/07/28

Abstract

Motivated by the concept of clean ideals, we introduce the notion of nil clean ideals of a ring. We define an ideal I of a ring R to be nil clean ideal if every element of I can be written as a sum of an idempotent and a nilpotent element of R. In this article we discuss various properties of nil clean ideals.

Related

• Weak Nil Clean Ideal
• Weak Nil Clean Rings
• Rings in which every element is either a sum or a difference of a nilpotent and an idempotent
• Weakly Clean Ideal
• Nil-good and nil-good clean matrix rings