Abstract:
We investigate the rank properties of the semigroup reducts of the affine
near-semiring A+
(Bn) over the Brandt semigroup Bn.We determine the small, lower,
intermediate and large ranks of the additive semigroup reduct An, and find a lower
bound for the upper rank of An. In case n ≥ 6, we show that the lower bound is
actually equal to the upper rank. We also find the small, lower, and large ranks of the
multiplicative semigroup reduct Mn, and provide lower bounds for the intermediate
and upper ranks of Mn.