Maximal zero product subrings and inner ideals of simple rings

TL;DR

This paper classifies all maximal zero product subsets in simple rings and explores their relationship with maximal inner ideals of the associated Lie algebra, advancing understanding of ring structure and ideal theory.

Contribution

It provides a complete classification of maximal zero product subsets in simple rings and links these to maximal inner ideals in related Lie algebras.

Findings

Classified all maximal zero product subsets in simple rings.

Established connections between zero product subsets and inner ideals.

Enhanced understanding of the structure of simple rings and their Lie algebra counterparts.

Abstract

Let Q be a (non-unital) simple ring. A nonempty subset S of Q is said to have zero product if S^2=0. We classify all maximal zero product subsets of Q. We also describe the relationship between the maximal zero product subsets of Q and the maximal inner ideals of its associated Lie algebra.