Rank properties of the semigroup reducts of affine near-semirings over Brandt semigroups

摘要

We investigate the rank properties of the semigroup reducts of the affine near-semiring over the Brandt semigroup . We determine the small, lower, intermediate and large ranks of the additive semigroup reduct , and find a lower bound for the upper rank of . In case , 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 , and provide lower bounds for the intermediate and upper ranks of .