Showing papers on "Bicyclic semigroup published in 1984"

Commutative Semigroup Rings

Abstract: "Commutative Semigroup Rings" was the first exposition of the basic properties of semigroup rings. Gilmer concentrates on the interplay between semigroups and rings, thereby illuminating both of these important concepts in modern algebra.

Languages and Inverse Semigroups

Abstract: We show how several famous combinatorial sequences appear in the context of nilpotent elements of the full symmetric inverse semigroup I Sn. These sequences appear either as cardinalities of certain nilpotent subsemigroups or as the numbers of special nilpotent elements and include the Lah numbers, the Bell numbers, the Stirling numbers of the second kind, the binomial coefficients and the Catalan numbers.

The centre of the second dual of a commutative semigroup algebra

Abstract: If S is an infinite, discrete, commutative semigroup then the semigroup algebra l1(S) is a commutative Banach algebra. Its dual is l∞(S), which is isometrically iso-morphic to C(βS), the space of continuous functions on the Stone-Cech compactification of S. This fact enables us to identify the second dual of l1(S) with M(βS), the space of bounded regular Borel measures on βS. Endowed with the Arens product the second dual is also a Banach algebra, so it is natural to ask whether a product may be defined in M(βS) without reference to l1(S). In §4 this is shown to be possible even when S is a non-discrete semitopological semigroup, provided that the operation in S may be extended to make βS into a left-topological semigroup in the manner of, for example, [2] where further references may be found. (Note, however, that the construction there is of a right-topological semigroup.) Having done this we may use results on βS to provide information about the measure algebra.

Semigroup algebras of finite inverse semigroups over arbitrary fields

Abstract: In the contracted semigroup algebra A of a finite inverse semigroup S over an arbitrary field there is given a basis, whose elements together with the zero of the algebra A form a semigroup ¯S, which is the 0-direct union of Brandt semigroups, whose description is given in terms of the semigroup S. With the help of this basis there is found the number of nonzero irreducible modular representations of the semigroup S by matrices over an algebraically closed field of nonzero characteristic.

Embedding recursively defined inverse semigroups in finitely presented semigroups

Abstract: By an inverse semigroup we mean an algebraic system of signature <,, axioms of an inverse semigroup are satisfied (cf. [i]). The term "recursively defined inverse semigroup" means an inverse semigroup having no more than countably many generators numbered by natural numbers and admitting, in the variety of all inverse semigroups, a recursively enumerabie set of defining relations in these generators (relative to some effective numeration of all word equalities).

Characters and the structure of finite semigroups

Abstract: It is shown that properties of the structure of a finite semigroup S such as the order of the set ofJ of S and the existence of normal subsemigroups may be deduced from the knowledge of the characters of the irreducible representations of S. The character table of the full transformation semigroup T4 of a four-element set is given.

Structure of monogenic inverse semigroups

Abstract: Some properties of monogenic inverse semigroups are considered. In particular, in a free monogenic inverse semigroup we study the disposition of idempotents, describe the structure of ideals, classify the congruences.