Nil Clean Ideal
Ajay Sharma, Dhiren Kumar Basnet

TL;DR
This paper introduces the concept of nil clean ideals in rings, where each element can be expressed as a sum of an idempotent and a nilpotent, and explores their properties.
Contribution
It defines nil clean ideals and investigates their fundamental properties, expanding the understanding of ring ideal structures.
Findings
Nil clean ideals are characterized by their elements being sums of idempotents and nilpotents.
Various properties and structural aspects of nil clean ideals are established.
The paper provides foundational insights into the behavior of nil clean ideals in ring theory.
Abstract
Motivated by the concept of clean ideals, we introduce the notion of nil clean ideals of a ring. We define an ideal of a ring to be nil clean ideal if every element of can be written as a sum of an idempotent and a nilpotent element of . In this article we discuss various properties of nil clean ideals.
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Taxonomy
TopicsPhysics and Engineering Research Articles
