Showing papers on "Bicyclic semigroup published in 1992"

The Adjoint of a Semigroup of Linear Operators

Abstract: The adjoint semigroup.- The ?(X,X?)-topology.- Interpolation, extrapolation and duality.- Perturbation theory.- Dichotomy theorems.- Adjoint semigroups and the RNP.- Tensor products.- The adjoint of a positive semigroup.

Semigroup algebras of the full matrix semigroup over a finite field

Abstract: Let M denote the multiplicative semigroup of all n-by-n matrices over a finite field F and K a commutative ring with an identity element in which the characteristic of F is a unit. It is proved here that the semigroup algebra K[M] is the direct sum of n + 1 algebras, namely, of one full matrix algebra over each of the group algebras K[GL(r, F)] with r = 0, 1, ..., n . The degree of the relevant matrix algebra over K[GL(r, F)] is the number of r-dimensional subspaces in an n-dimensional vector space over F. For K a field of characteristic different from that of F, this result was announced by Faddeev in 1976. He only published an incomplete sketch of his proof, which relied on details from the representation theory of finite general linear groups. The present proof is self-contained.

Semigroups of left quotients―the uniqueness problem

Abstract: Let S be a subsemigroup of a semigroup Q. Then Q is a semigroup of left quotients of S if every element of Q can be written as a*b, where a lies in a group J^-class of Q and a* is the inverse of a in this group; in addition, we insist that every element of S satisfying a weak cancellation condition named square-cancellable lie in a subgroup of Q. J. B. Fountain and M. Petrich gave an example of a semigroup having two non-isomorphic semigroups of left quotients. More positive results are available if we restrict the classes of semigroups from which the semigroups of left quotients may come. For example, a semigroup has at most one bisimple inverse wsemigroup of left quotients. The crux of the matter is the restrictions to a semigroup S of Green's relations 3? and if in a semigroup of quotients of S. With this in mind we give necessary and sufficient conditions for two semigroups of left quotients of S to be isomorphic under an isomorphism fixing S pointwise. The above result is then used to show that if R is a subring of rings Q, and Q2 and the multiplicative subsemigroups of Q, and Q2 are semigroups of left quotients of the multiplicative semigroup of R, then Q, and Q2 are isomorphic rings.

The minimal degree of a finite inverse semigroup

Abstract: The minimal degree of an inverse semigroup S is the minimal cardinality of a set A such that S is isomorphic to an inverse semigroup of one-to-one partial transformations of A. The main result is a formula that expresses the minimal degree of a finite inverse semigroup S in terms of certain subgroups and the ordered structure of S. In fact, a representation of S by one-to-one partial transformations of the smallest possible set A is explicitly constructed in the proof of the formula. All known and some new results on the minimal degree follow as easy corollaries

Distributive monoid algebras

Abstract: All rings are assumed to be associative with a nonzero unity element, and modulles and subrings are assumed to be unital. A distributive module is a module with a distributive lattice of submodules. Right distributive monoid rings were studied in [1-6] under !various additional conditions. A monoid (ring) G is called regular if for any element f there exists an element g such that f = fgf. Our main results are Theorems 1 and 2.

On rigid monoids and 2-fir monoid rings

Abstract: It is proved that the universal group of a torsion free rigid monoid is torsion free. As a consequence, a new condition on a monoid M for the monoid ring R[M] to be a 2-fir is given. Furthermore, the monoids between a rigid monoid and its universal group are studied.

The regular radical of semigroup rings of commutative semigroups

Abstract: A description of regular group rings is well known (see [12]). Various authors have considered regular semigroup rings (see [17], [8], [10], [11], [4]). These rings have been characterized for many important classes of semigroups, although the general problem turns out to be rather difficult and still has not got a complete solution. It seems natural to describe the regular radical in semigroup rings for semigroups of the classes mentioned. In [10], the regular semigroup rings of commutative semigroups were described. The aim of the present paper is to characterize the regular radical ρ( R [ S ]) for each associative ring R and commutative semigroup S .

Monoid of Multisets and Subsets

Abstract: Summary. The monoid of functions yielding elements of a group is introduced. The monoid of multisets over a set is constructed as such monoid where the target group is the group of natural numbers with addition. Moreover, the generalization of group operation onto the operation on subsets is present. That generalization is used to introduce the group 2 G of subsets of a group G. MML Identifier: MONOID 1.

Preaffine semigroups and convex matrix semigroups

Abstract: Algebraic conditions are given which guarantee that a semigroup on a subset of real topological vector space can be embedded in a convex matrix semigroup. We also study when the minimal ideal of a convex matrix semigroup will be convex.