Let R be an hereditary Noetherian prime ring, let S be a "Dedekind closure" of R and let T be the category of finitely generated S-torsion R-modules. It is shown that for all i ~ 0, there is an exact sequence 0 -> Ki(T) -> Ki(R) -> Ki(S) ...... O. If i = 0, or R has finitely many idempotent ideals then this sequence splits. A notion of ''right ideal class group" is then introduced for hereditar...

for any given finite abelian group‎, ‎we give factorizations of the group determinant in the group algebra of any subgroups‎. ‎the factorizations is an extension of dedekind's theorem‎. ‎the extension leads to a generalization of dedekind's theorem‎.

Abstract. Dedekind symbols are generalizations of the classical Dedekind sums (symbols). There is a natural isomorphism between the space of Dedekind symbols with Laurent polynomial reciprocity laws and the space of modular forms. We will define a new elliptic analogue of the Apostol-Dedekind sums. Then we will show that the newly defined sums generate all odd Dedekind symbols with Laurent poly...

For a given family (Gi)i∈N of finitely generated abelian groups, we construct Dedekind domain D having the following properties. Pic(D)≅⨁i∈NGi. each i∈N, there exists submonoid Si⊆D• with Pic(DSi)≅Gi. Each class Pic(D) and all Pic(DSi) contains infinitely many prime ideals.

Motivated by symbolic dynamics, we study the problem, given a unital subring 5 of the reals, when is a matrix A algebraically shift equivalent over S to a primitive matrix? We conjecture that simple necessary conditions on the nonzero spectrum of A are sufficient, and establish the conjecture in many cases. If S is the integers, we give some lower bounds on sizes of realizing primitive matrices...

It was shown in [13] that very large classes of nonlinear PDEs have solutions which can be assimilated with usual measurable functions on the Euclidean domains of definition of the respective equations. In this paper the regularity of these solutions has significantly been improved by showing that they can in fact be assimilated with Hausdorff continuous functions. The method of solution of PDE...