Identities in Brandt semigroups, revisited

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.