Rings of arithmetic functions

Arithmetic of Circular Rings

Circular arithmetic, introduced by I. Gargantini and P. Henrici [2J as an extension of the complex arithmetic, provided the formulati­ on of methods for solving some problems of computational complex anal­ ysis (e. g. tl:e inclusion of the polynomial complex zeros [2J, [3J, cir­ cular approximation of the closed regions in the complex plane [IJ, [4J , ~J, [8J, the evaluations of complex functio...

Arithmetic Convolution Rings

Arithmetic convolution rings provide a general and unified treatment of many rings that have been called arithmetic; the best known examples are rings of complex valued functions with domain in the set of non-negative integers and multiplication the Cauchy product or the Dirichlet product. The emphasis here is on factorization and related properties of such rings which necessitates prior result...

Generalized Rings of Measurable and Continuous Functions

This paper is an attempt to generalize, simultaneously, the ring of real-valued continuous functions and the ring of real-valued measurable functions.

Rings of Quotients of Rings of Functions

The Λ - Dimension of Commutative Arithmetic Rings

It is shown that every commutative arithmetic ring R has λ-dimension ≤ 3. An example of a commutative Kaplansky ring with λ-dimension 3 is given. Moreover, if R satisfies one of the following conditions, semi-local, semi-prime, self f p-injective, zero-Krull dimensional, CF or FSI then λ-dim(R) ≤ 2. It is also shown that every zero-Krull dimensional commu-tative arithmetic ring is a Kaplansky r...