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arXiv · 1308.4087

The Ranks of the Additive Semigroup Reduct of Affine Near-Semiring over Brandt Semigroup

Jitender Kumar·K. V. Krishna
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Abstract

This work investigates the rank properties of $A^+(B_n)$, the additive semigroup reduct of affine near-semiring over Brandt semigroup $B_n$. In this connection, this work reports the ranks $r_1$, $r_2$, $r_3$ and $r_5$ of $A^+(B_n)$ and identifies a lower bound for the upper rank $r_4(A^+(B_n))$. While this lower bound is found to be the $r_4(A^+(B_n))$ for $n \ge 6$, in other cases where $2 \le n \le 5$, the upper rank of $A^+(B_n)$ is still open for investigation.

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Jitender Kumar, K. V. Krishna. 2013-08-19. The Ranks of the Additive Semigroup Reduct of Affine Near-Semiring over Brandt Semigroup. https://arxiv.org/abs/1308.4087

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