It is well-known that, given a Dedekind categoryR the category of (typed) matrices with coefficients from R is a Dedekind category with arbitrary relational sums. In this paper we show that under slightly stronger assumptions the converse is also true. Every atomic Dedekind category R with relational sums and subobjects is equivalent to a category of matrices over a suitable basis. This basis i...

in this paper we study the concept of ph-biatness ofa banach algebra a, where ph is a continuous homomorphism on a.we prove that if ph is a continuous epimorphism on a and a hasa bounded approximate identity and a is ph- biat, then a is ph-amenable. in the case where ph is an isomorphism on a we showthat the ph- amenability of a implies its ph-biatness.

Abstract Let $$ \gcd (k,j) gcd ( k , j ) denote the greatest common divisor of integers k and j , let r be any fixed positive integer. Define $$\begin{aligned} M_r(x; f) := \sum _{k\le x}\frac{1}{k^{r+1...

We study the relation of the ideal class group of a Dedekind domain A to that of As, where S is a multiplicatively closed subset of A. We construct examples of (a) a Dedekind domain with no principal prime ideal and (b) a Dedekind domain which is not the integral closure of a principal ideal domain. We also obtain some qualitative information on the number of non-principal prime ideals in an ar...

The regulation of proton transport and cytosolic pH was studied in rat papillary collecting duct (PCD) cells in culture using a pH-sensitive fluorescence probe, 2,7-bis-carboxyethyl-5,6-carboxyfluorescein (BCECF). Data were obtained from confluent monolayers grown on glass coverslips and dipped in a HCO3- -free medium, pH 7.40. The resting intracellular pH (pHi) was 7.16 +/- 0.03 (n = 20). When...

It is well-known that, given a Dedekind category R the category of (typed) matrices with coeecients from R is a Dedekind category with arbitrary relational sums. In this paper we show that under slightly stronger assumptions the converse is also true. Every atomic Dedekind category R with relational sums and subobjects is equivalent to a category of matrices over a suitable basis. This basis is...

Proof. We will calculate the integral closure of A inside K. We begin with a more general discussion. Suppose C is an irreducible, affine curve, that is, C is some irreducible affine variety of dimension 1. Let A be the ring of regular functions on C, so that A is a noetherian domain of Krull dimension 1. Localization preserves the noetherian condition, as well as the domain condition. Thus, th...