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

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.

Contributed talk titled "On the Ranks of Additive Semigroup Reducts of Affine Near-Semirings over Brandt Semigroups" the Conference General Algebra and Its Applications: GAIA 2013, Melbourne, Australia, July 15-19, 2013

References in corpus (1)

• Affine Near-Semirings over Brandt Semigroups

Cited by in corpus (2)

• Rank Properties of Multiplicative Semigroup Reduct of Affine Near-Semirings over $B_n$
• The Large Rank of a Finite Semigroup using Prime Subsets