In this paper we solve moment problems for Poisson transforms and, more generally, for completely positive linear maps on unital C∗-algebras generated by “universal” row contractions associated with F+n , the free semigroup with n generators. This class of C ∗-algebras includes the Cuntz-Toeplitz algebra C∗(S1, . . . , Sn) (resp. C ∗(B1, . . . , Bn)) generated by the creation operators on the f...

A rst explicit connection between nitely presented commutative monoids and ideals in polynomial rings was used 1958 by Emelichev yielding a solution to the word problem in commutative monoids by deciding the ideal membership problem. The aim of this paper is to show in a similar fashion how congruences on monoids and groups can be characterized by ideals in respective monoid and group rings. Th...

let $l$ be a completely regular frame and $mathcal{r}l$ be the ‎ring of continuous real-valued functions on $l$‎. ‎we show that the‎ ‎lattice $zid(mathcal{r}l)$ of $z$-ideals of $mathcal{r}l$ is a‎ ‎normal coherent yosida frame‎, ‎which extends the corresponding $c(x)$‎ ‎result of mart'{i}nez and zenk‎. ‎this we do by exhibiting‎ ‎$zid(mathcal{r}l)$ as a quotient of $rad(mathcal{r}l)$‎, ‎the‎ ‎...

We give an alternative treatment and extension of some results of Itoh and Mahmoud on one-sided interval trees. The proofs are based on renewal theory, including a case with mixed multiplicative and additive renewals.

Let S be a set of n ideals of a commutative ring A and let Geven (respectively Godd) denote the product of all the sums of even (respectively odd) number of ideals of S. If n ≤ 6 the product of Geven and the intersection of all ideals of S is included in Godd. In the case A is an Noetherian integral domain, this inclusion is replaced by equality if and only if A is a Dedekind domain.

The concept of a 0-distributive poset is introduced. It is shown that a section semicomplemented poset is distributive if and only if it is 0-distributive. It is also proved that every pseudocomplemented poset is 0-distributive. Further, 0-distributive posets are characterized in terms of their ideal lattices.

A left ideal of any C∗-algebra is an example of an operator algebra with a right contractive approximate identity (r.c.a.i.). Indeed, left ideals in C∗-algebras may be characterized as the class of such operator algebras, which happen also to be triple systems. Conversely, we show here and in a sequel to this paper, that operator algebras with r.c.a.i. should be studied in terms of a certain le...

Let G be a torsionfree compact p-adic analytic group. We give sufficient conditions on p and G which ensure that the Iwasawa algebra ΩG of G has no non-trivial two-sided reflexive ideals. Consequently, these conditions imply that every nonzero normal element in ΩG is a unit. We show that these conditions hold in the case when G is an open subgroup of SL2(Zp) and p is arbitrary. Using a previous...