We compare several different concepts of integer-valued polynomials on algebras and collect the few results and many open questions to be found in the literature. (2000 Math. Subj. Classification: Primary 13F20; Secondary 16S50, 13B25, 13J10, 11C08, 11C20)

A triangular limit algebra A is isometrically isomorphic to the tensor algebra of a C∗-correspondence if and only if its fundamental relation R(A) is a tree admitting a Z+0 -valued continuous and coherent cocycle. For triangular limit algebras which are isomorphic to tensor algebras, we give a very concrete description for their defining C∗-correspondence and we show that it forms a complete in...

A charge (finitely additive measure) defined on a Boolean algebra of sets taking values in a group G is called a strictly nonzero (SNZ) charge if it takes the identity value in G only for the zero element of the Boolean algebra. A study of such charges was initiated by Rudiger Göbel and KPS Bhaskara Rao in 2002 [3]. Our main result is a solution to one of the questions posed in that paper: we s...

Article history: Received 15 November 2010 Available online 13 October 2011 Communicated by Luchezar L. Avramov MSC: 13F05 11C08 13F20 13G05 13B25

The classical ring of integer-valued polynomials Int(Z) consists of the polynomials in Q[X] that map Z into Z. We consider a generalization of integervalued polynomials where elements of Q[X] act on sets such as rings of algebraic integers or the ring of n× n matrices with entries in Z. The collection of polynomials thus produced is a subring of Int(Z), and the principal question we consider is...

A new model of coupled oscillators is proposed and investigated. All phase variables and parameters are integer-valued. The model is shown to exhibit two types of motions, those which involve periodic phase differences, and those which involve drift. Traditional dynamical concepts such as stability, bifurcation and chaos are examined for this class of integer-valued systems. Numerical results a...