Syntactic semigroup problem for the semigroup reducts of Affine Near-semirings over Brandt Semigroups

TL;DR

This paper investigates whether certain semigroup reducts of affine near-semirings over Brandt semigroups are syntactic, establishing that they are indeed syntactic semigroups, thus contributing to algebraic semigroup theory.

Contribution

It proves that the semigroup reducts of affine near-semirings over Brandt semigroups are syntactic semigroups, addressing a specific open problem in algebraic semigroup theory.

Findings

Both semigroup reducts of A^+(B_n) are syntactic semigroups.

The work advances understanding of the algebraic structure of affine near-semirings.

Provides a method to identify syntactic semigroups in this context.

Abstract

The syntactic semigroup problem is to decide whether a given finite semigroup is syntactic or not. This work investigates the syntactic semigroup problem for both the semigroup reducts of $A^+(B_n)$, the affine near-semiring over a Brandt semigroup $B_n$. It is ascertained that both the semigroup reducts of $A^+(B_n)$ are syntactic semigroups.