Affine Near-Semirings over Brandt Semigroups

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The thesis aims at studying various structural properties of affine near-semirings over Brandt semigroups. The study considers various aspects, viz. semigroup theoretic properties, ring theoretic properties and formal language theoretic connections. At the outset, the thesis classifies the elements of an affine near-semiring over Brandt semigroup, denoted by A+(Bn), and finds the cardinality of A+(Bn), for an arbitrary natural number n. In order to ascertain the semigroup theoretic properties of A+(Bn), the thesis completely characterizes the Green relations on both of its semigroup reducts. The thesis reveals that the additive semigroup reduct is eventually regular and the multiplicative semigroup reduct is orthodox. Further, the rank properties of these semigroup reducts are investigated in detail. By determining all right ideals, ideals and radicals, the thesis studies the ring theoretic structure of A+(Bn). The study establishes certain formal language theoretic connections to A+(Bn) by showing that both of its semigroup reducts are syntactic semigroups.
Supervisor: K.V. Krishna