The term The Theory of Rings seems first used as title of a book by Jacobson [43], and in his
preface Jacobson asserts that the theory that forms the subject of the book had its beginning …

Going-down rings are characterized in terms of the AV-domains of Akiba. As a result, the
internal characterization of going-down rings which has recently been established by …

This paper deals with two themes involving the going down (GD) behavior of the overrings of
a domain R. First, as illustrated by several results in [3] and [4], hypotheses about GD often …

Let V be a valuation ring of the form K+M, where K is a field and M(≠0) is the maximal ideal
of V. Let D be a proper subring of K. Necessary and sufficient conditions are given that the …

Given two homomorphisms of rings j1: R1→ R'and j2: R2→ R'we may construct a new ring R
called the pullback of R1 and R2 over R', together with homomorphisms i1: R→ R1 and i2 …

This article explores several extensions of the Prüfer domain notion to rings with zero
divisors. These extensions include semihereditary rings, rings with weak global dimension …

In this paper we will sharpen Wiseman's upper bound on the global dimension of a fibre
product [Theorem 2] and use our bound to compute the global dimension of some examples …

The study of global dimension of pullback rings has been subject of several interesting
works and has been served to solve many open problems. In this paper, we attempt to …

In this paper we deal with the study of pairs of rings where all intermediate rings are Jaffard.
Furthermore, we introduce a new invariant allowing us to compute the number of Jaffard …

Le but de ce papier est celui de développer la théorie des anneaux de pseudo-valuation, au
sens de HEDSTROM-HOUSTON [24] qui les ont introduits, compte tenu de quelques …