On Weak Regular ^＊-semigroups

In this paper, a special kind of partial algebras called projective partial groupoids is defined.It is proved that the inverse image of all projections of a fundamental weak regular ^*-semigroup under the homomorphism induced by the maximum idempotent-separating congruence of a weak regular ^*-semigroup has a projective partial groupoid structure. Moreover, a weak regular ^*-product which connects a fundamental weak regular ^*-semigroup with corresponding projective partial groupoid is defined and characterized. It is finally proved that every weak regular ^*-product is in fact a weak regular ^*-semigroup and any weak regular ^*-semigroup is constructed in this way.     

*-Simple typeA ω-semigroups

Communicated by N. R. Reilly     

Pontryagin space structure in reproducing kernel Hilbert spaces over *-semigroups

The geometry of spaces with indefinite inner product, known also as Krein spaces, is a basic tool for developing Operator Theory therein. In the present paper we establish a link between this geometry and the algebraic theory of *-semigroups. It goes via the positive definite functions and related to them reproducing kernel Hilbert spaces. Our concern is in describing properties of elements of the semigroup which determine shift operators which serve as Pontryagin fundamental symmetries.     

Extension of irreducible characters from normal subgroups

Let G = NH(NΔG) be a finite group and let x be an invariant irreducible character of N. A sufficient condition is provided for x to be extended to a character of G.     

Multilinearity partitions of characters of embedded groups *

We show that a well-known polarization formula for Hermitian inner products on complex vector spaces generalizes to the case of inner products on Clifford modules. This observation allows us to conclude that norm-preserving linear maps of Clifford modules necessarily preserve the inner product. These results hold for modules over the quaternious as a special case.     

RGC n -commutative Δ-semigroups

S is called a δ-semigroup if the lattice of all congruences of S is a chain with respect to inclusion. In the literature there are lots of papers which investigate the δ-semigroups in special classes of semigroups ([1], [3], [5], [6], [10], [11], [12], [14],). In this paper we describe the RGC _n -commutative δ-semigroups.     

Regular Bisimple ω2-semigroups

The regular semigroups S with an idempotent set Es = {e0,e1,…,en,…} such that e0 ＞ e1 ＞…＞ en ＞… is called a regular ω-semigroup. In [5] Reilly determined the structure of a regular bisimple ω-semigroup as BR(G,θ),which is the classical Bruck-Reilly extension of a group G.     

Computing denumerants in numerical 3-semigroups

Abstract

As far as we know, usual computer algebra packages can not compute denumerants for almost medium (about a hundred digits) or almost medium-large (about a thousand digits) input data in a reasonably time cost on an ordinary computer. Implemented algorithms can manage numerical n-semigroups for small input data.

Basically, the denumerant of a non-negative element s ∈ ? is the number of non-negative integer solutions of certain linear non-negative Diophantine equation which constant term is equal to s.

Here we are interested in denumerants of numerical 3-semigroups which have almost medium input data. A new algorithm for computing denumerants is given for this task. It can manage almost medium input data in the worst case and medium-large or even large input data in some cases.