On the Fourier transformation of positive,positive definite measures on commutative hypergroups,and dual convolution structures

We show that the support of the Fourier transform of a positive, positive definite measure on a commutative hypergroupK contains a positive character. This generalizes the known fact that the support of the Plancherel measure π contains a positive character (which in general is not the identity character1). It follows that contains a positive character for whenever a dual convolution exists. In particular, if1∈supp π, then1 is this character. We also give some further general results about the support of dual convolution products in terms ofsupp π. Some examples associated with Gelfand pairs and, in particular, non-compact Riemannian symmetric spaces of rank 1 are discussed.     

On divided commutative rings

Let R be a commutative ring with identity having total quotient ring T. A prime ideal P of R is called divided if P is comparable to every principal ideal of R. If every prime ideal of R is divided, then R is called a divided ring. If P is a nonprincipal divided prime, then P^-1 = { x ? T : xP ? P} is a ring. We show that if R is an atomic domain and divided, then the Krull dimension of R ≤ 1. Also, we show that if a finitely generated prime ideal containing a nonzerodivisor of a ring R is divided, then it is maximal and R is quasilocal.     

On power commutative semigroups

Communicated by G. Lallement     

On commutative Kleene monoids

Commutative Kleene monoids are rational     

On probabilistic commutative spaces

A new characterization is given for the probabilistic commutative Riemannian spaces studied originally (in the compact case) by Roberts and Ursell. Moreover, some earlier basic results are generalized to the non-compact case.     

On weakly commutative peo-semigroups

Communicated by Robert McFadden     

On lattice-ordered commutative semigroups

Decompositions of elements into intersections of primal elements and into intersections of p-components are studied in certain lattice-ordered commutative semigroups, by making use of the new development in commutative ideal theory without finiteness conditions, due to Fuchs-Heinzer-Olberding [7]. Several results concerning ideals can be phrased as theorems in abstract ideal theory.The intersections we consider are in general not irredundant, and the associated prime elements are not unique. However, one can establish a canonical intersection that is often irredundant with uniquely determined associated primes.     

Decomposition of conditionally positive definite functions on commutative hypergroups

In this paper we consider bounded, conditionally positive definite functions on commutative hypergroups. We show an integral representation that allows to decompose conditionally positive definite functions as differences of positive definite functions.     

Decomposition of conditionally positive definite functions on commutative hypergroups

In this paper we consider bounded, conditionally positive definite functions on commutative hypergroups. We show an integral representation that allows to decompose conditionally positive definite functions as differences of positive definite functions.     

On free commutative regular rings

It has been observed that the category of all regular rings, when viewed as a full subcategory of the category of all rings, is not an algebraic variety. However if a regular ring is viewed as a ring equipped with a unary operation q such that xx^qx = x and 0000^q= 0, then the category of all rings with this added structure is indeed a variety but it is not, in any natural way, a subcategory of the category of all rings. In this article regular rings are viewed in this way and the free commutative regular rings are constructed. They are derived from the universal commutative regular ring associated with certain polynomial rings.     

On morphisms of commutative monoids

The aim of this work is to study monoid morphisms between commutative monoids. Algorithms to check if a monoid morphism between two finitely generated monoids is injective and/or surjective are given. The structure of the set of monoid morphisms between a monoid and a cancellative monoid is also studied and an algorithm to obtain a system of generators of this set is provided.