On the sum of annihilators in nearrings

Abstract

A ring is termed a left IN-ring if the right annihilator of the intersection of any two left ideals is equal to the sum of their right annihilators. As a generalization of left IN-ring, a ring is called a right SA-ring if the sum of the right annihilators of any two ideals forms the right annihilator of an ideal. While extensive research has been conducted on the IN and SA properties for rings, these concepts have not been explored for nearrings, revealing a gap in the current literature. This paper aims to extend and study these properties within the framework of nearrings. One of our main results investigates the relationship between the IN and SA properties of a ring R and those of the zero-symmetric nearring of polynomials and formal power series over R, where “substitution” serves as its “multiplication” operation. Additionally, we present several examples to support and illustrate our results.