Description Of Ring Research Articles

Rings of formal matrices close to regular

We give a description of rings of formalmatrices belonging to one of the following classes of rings: semiartinian rings, max-rings, V -rings, SV -rings. We study semiartinian SSP-rings and SSP-rings of formal matrices.

I*0-Modules

We study rings over which every module is an I*0 -module dual to I0-module. We describe semiregular rings over which every module is at the same time I*0 -module and I0-module. We give a description of rings over which every module is a direct sum of injective module and SV -module. We investigate relations between weakly Baer modules and I*0 -modules.

Quasi-Endomorphism Rings of Almost Completely Decomposable Torsion-Free Abelian Groups of Rank 4 With Zero Jacobson Radical

In this paper, a description of rings of quasi-endomorphisms of almost completely decomposable torsion-free Abelian groups of rank 4 with zero Jacobson radical is obtained.

An arithmetic characterization of algebraic number fields with a given class group

Let R be the ring of integers of a number field K with class group G. It is classical that R is a unique factorization domain if and only if G is the trivial group; and the finite abelian group G is generally considered as a measure of the failure of unique factorization in R. The first arithmetic description of rings of integers with non-trivial class groups was given in 1960 by L. Carlitz (1). He proved that G is a group of order ≤ two if and only if any two factorizations of an element of R into irreducible elements have the same number of factors. In ((6), p. 469, problem 32) W. Narkiewicz asked for an arithmetic characterization of algebraic number fields K with class numbers ≠ 1, 2. This problem was solved for certain class groups with orders ≤ 9 in (2), and for the case that G is cyclic or a product of k copies of a group of prime order in (5). In this note we solve Narkiewicz's problem in general by giving arithmetical characterizations of a ring of integers whose class group G is any given finite abelian group.

ALMOST-SEMISIMPLE RINGS

In this report there is given a full description of rings over which each module is the sum of an injective and a projective submodule. Bibliography: 12 references.