Because traditional ring theory places restrictive hypotheses on all submodules of a module,
its results apply only to small classes of already well understood examples. Often, modules …

, Coldie defined the reduced rank p (M) of af initely generated module M over a edprime
Coldie ring R to be the uniform dimension of M/y (If), where y is the Goldie torsion radial …

Jategaonkar'2, Pro~ osition 1.9 has snown that if P is a minimal wime ideal of a left
Noetherian ring R, then 9 has finite length with resgect to the torsion radical defined at P. On …

The definition of a class of module as well as submodule namely (bounded module and
bounded submodule) has introduced in various ways. In this study, we concentrate on some …

When multiplication of topologizing filters is commutative Page 1 Journal of Pure and
Applied Algebra 140 (1999) 87–105 When multiplication of topologizing filters is …

A module M is called product closed if every hereditary pretorsion class in σ [M] is closed
under products in σ [M]. Every module M which is locally of finite length (every finitely …

Let R be a right noetherian ring. A module MR is called a Δ-module provided R satisfies the
descending chain condition for annihilators of subsets of M. For a Δ-module, a series 0⊂ M …

The set Fil RR of all right topologizing filters on a fixed, but arbitrary ring R is both a complete
lattice under inclusion and a monoid with respect to an order compatible, but in general …

La notion de module C-injectif a 6t4 introduite par i'aith dans [5 1; 114tude de cea modules
Btant ult4rieurement ddveloppde dans beaucoup de travaux (voir par exemple [3 I,[6 …

Let R be an associative ring and let us denote by R-mod the category of all unital left
modules. Let (T, F) be an hereditary torsion theory of modules with torsion class T and …