Semidistributive nearrings with identity

TL;DR

This paper proves that semidistributive nearrings with identity have an abelian additive group, and under certain conditions, are actually associative rings, advancing the understanding of their algebraic structure.

Contribution

It establishes that semidistributive nearrings with identity are abelian and, without elements of order 2, are associative rings, providing new structural insights.

Findings

Additive group of such nearrings is abelian.

If no elements of order 2, the nearring is an associative ring.

Structural properties depend on the presence of elements of order 2.

Abstract

It is proved that the additive group of every semidistributive nearring $R$ with an identity is abelian and if R has no elements of order $2$, then the nearring $R$ actually is an associative ring.