A useful and simple idea in determining the representation type of an artinian ring A is to
relate its module category mod (A) with a module category of another ring A'whose …

We show that if a class of modules is closed under pure quotients, then it is precovering if
and only if it is covering, and this happens if and only if it is closed under direct sums. This is …

This paper is concerned with the omnipresence of the formation of the subcategories right
(left) perpendicular to a subcategory of objects in an abelian category. We encounter these …

In this paper divisible and codivisible modules are studied relative to a torsion theory on
Mod. fi. It is shown, for example, that if the tor sion theory is hereditary, then the following are …

Ddmtr (j) ialls; L class 7 111 the category of unital left R-modules fcwsimr ii 57 IS closed
under homomorphic images. direr t sum and extensions of one module in 7 by another. A …

On rings with trivial torsion parts Page 1 BULL. AUSTRAL. MATH. SOC. I8A40 VOL. 9 (1973),
275-290. (I6AI2 ' 16A32) On rings with trivial torsion parts L. Bican, P. Jambor, T. Kepka, P …

For a ring R with unit, let RM denote the category of unitary left R-modules. Following SE
Dickson [3], a (non-empty) class of R-modules is a torsion class in rM if is closed under …

Let R be an associative ring with unit element. Mod-R and R-Mod will denote the categories
of unitary right and left R-modules, respectively, and all modules are assumed to be in Mod …

Let $ R $ be the quotient of a regular coherent commutative ring by a finitely generated
ideal. In this paper, we classify all abelian subcategories of finitely presented $ R $-modules …

1. Introduction. Let R be a ring (associative and with identity). It is easy to see that every left
ideal of R is the (left) annihilator of a finite subset of R if and only if every cyclic left R-module …