# Identities in Brandt semigroups, revisited

## TL;DR

This paper offers a new proof for the identity basis of Brandt semigroups over finite exponent groups, addressing gaps in previous proofs and enhancing understanding of their algebraic structure.

## Contribution

It provides a new, rigorous proof for the identity basis of Brandt semigroups over finite exponent groups, clarifying previous gaps in the literature.

## Key findings

- Established an identity basis for Brandt semigroups over finite exponent groups
- Filled a gap in the original proof from 1985
- Enhanced the theoretical understanding of Brandt semigroup identities

## Abstract

We present a new proof for the main claim made in the author's paper "On the identity bases of Brandt semigroups" (Ural. Gos. Univ. Mat. Zap. 14, no.1 (1985), 38--42); this claim provides an identity basis for an arbitrary Brandt semigroup over a group of finite exponent. We also show how to fill a gap in the original proof of the claim in loc. cit.