All rings in this discussion are commutative with unity, and all modules are unital. The
purpose of this paper is to study the structure of those rings whose modules satisfy the …

In analogy to the elementwise definition of von Neumann regular rings an $ R $-module $ M
$ is called regular if given any element $ m\in M $ there exists $ f\in {\operatorname {Hom} …

In this note we will make a few observations on the structure of fields and local rings. The
main point is to show that a weaker version of Cohen structure theorem for complete local …

Publisher Summary This chapter discusses the different aspects of idealizer rings. It is
assumed that S is a ring with an identity element, A a right ideal of S, and I (A)={s∈ Sl sA⊆ …

In this article we introduce the concept of $ r $-ideals in commutative rings (note: an ideal $ I
$ of a ring $ R $ is called $ r $-ideal, if $ ab\in I $ and ${\rm Ann}(a)=(0) $ imply that $ b\in I …

In [1],[2] and [3] no chain conditions occur anywhere; the strongest" finiteness condition"
which had to be postulated for certain parts of the theory was that the rings have nilpotent …

We prove that each almost local-global semihereditary ring R has the stacked bases
property and is almost Bézout. More precisely, if M is a finitely presented module, its torsion …

In [5], Skornyakov claims (as his main result) that a ring R is quasi-Frobenius and serial ("
generalised uniserial") if and only if every left R-module is a direct sum of left ideals …

A commutative ring S with identity element 1 is called an elementary divisor ring (resp.
Hermite ring) if for every matrix A over S there exist nonsingular matrices P, Q such that PAQ …