Affine Near-Semirings over Brandt Semigroups

Abstract

In order to study the structure of $A^{+}(B_n)$ -- the affine near-semiring over a Brandt semigroup -- this work completely characterizes the Green's classes of its semigroup reducts. In this connection, this work characterizes the elements of $A^{+}(B_n)$ and reports the size of $A^{+}(B_n)$. Further, idempotents and regular elements of the semigroup reducts of $A^{+}(B_n)$ have also been characterized and studied some relevant semigroups in $A^{+}(B_n)$.

Comm. Algebra, To appear

References in corpus (1)

• Rank Properties of Multiplicative Semigroup Reduct of Affine Near-Semirings over $B_n$

Cited by in corpus (7)

• The Ranks of the Additive Semigroup Reduct of Affine Near-Semiring over Brandt Semigroup
• Rank Properties of Multiplicative Semigroup Reduct of Affine Near-Semirings over $B_n$
• Algebraic aspects and functoriality of the set of affiliated operators
• Radicals and Ideals of Affine Near-semirings over Brandt Semigroups
• On the commuting graphs of Brandt semigroups
• Syntactic semigroup problem for the semigroup reducts of Affine Near-semirings over Brandt Semigroups
• Rank Properties of the Semigroup of Endomorphisms over Brandt semigroup