Rank Properties of Multiplicative Semigroup Reduct of Affine Near-Semirings over $B_n$

TL;DR

This paper studies the rank properties of the multiplicative semigroup reduct of affine near-semirings over an aperiodic Brandt semigroup, providing exact and bounded values for various ranks.

Contribution

It determines the small, lower, and large ranks of the semigroup and establishes lower bounds for intermediate and upper ranks, advancing understanding of its algebraic structure.

Findings

Small rank, lower rank, and large rank are explicitly obtained.

Lower bounds for intermediate and upper ranks are established.

The work enhances the algebraic understanding of affine near-semirings over $B_n$.

Abstract

This work investigates the rank properties of $A^+(B_n)$, the multiplicative semigroup reduct of the affine near-semirings over an aperiodic Brandt semigroup $B_n$. In this connection, the work obtains the small rank, lower rank and large rank of $A^+(B_n)$. Further, the work provides lower bounds for intermediate rank and upper rank of $A^+(B_n)$.