Affine Near-Semirings over Brandt Semigroups

TL;DR

This paper thoroughly analyzes the algebraic structure of affine near-semigroups over Brandt semigroups, providing detailed classifications and size calculations of their elements and Green's classes.

Contribution

It offers a complete characterization of Green's classes, elements, idempotents, and regular elements of the affine near-semiring over Brandt semigroups, advancing understanding of their algebraic structure.

Findings

Characterized Green's classes of the semigroup reducts

Determined the size of the affine near-semiring

Identified idempotents and regular elements

Abstract

In order to study the structure of $A^+(B_n)$ -- the affine near-semiring over a Brandt semigroup -- this work completely characterizes the Green's classes of its semigroup reducts. In this connection, this work characterizes the elements of $A^+(B_n)$ and reports the size of $A^+(B_n)$. Further, idempotents and regular elements of the semigroup reducts of $A^+(B_n)$ have also been characterized and studied some relevant semigroups in $A^+(B_n)$.