Abstract
We investigate the rank properties of the semigroup reducts of the affine near-semiring \(A^+(B_n)\) over the Brandt semigroup \(B_n\). We determine the small, lower, intermediate and large ranks of the additive semigroup reduct \(A_n\), and find a lower bound for the upper rank of \(A_n\). In case \(n \ge 6\), 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 \(M_n\), and provide lower bounds for the intermediate and upper ranks of \(M_n\).
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We would like to express our sincere gratitude to the referee for his/her insightful comments which helped us in improving the presentation of the paper.
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Communicated by Mikhail Volkov.
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Kumar, J., Krishna, K.V. Rank properties of the semigroup reducts of affine near-semirings over Brandt semigroups. Semigroup Forum 93, 516–534 (2016). https://doi.org/10.1007/s00233-016-9826-5
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DOI: https://doi.org/10.1007/s00233-016-9826-5