Nil Clean Ideal

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 $I$ 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.