Rings Characterized by Their Torsion Cyclic Modules Page 1 HOUSTON JOURNAL OF
MATHEMATICS, Volume 14, No. 3, 1988. RINGS CHARACTERIZED BY THEIR TORSION …

Commutative rings over which all torsion theories are hereditary Page 1 COMMUNICATIONS
IN ALGEBRA, 9(15), 1533-1540 (1981) COMMUTATIVE RINGS OVER WHICH ALL TORSION …

The theory of Loewy modules has occurred in many different contexts in the literature. W.
Krull used the notion of a Loewy module in some of bis studies ([7] and [8]) of ideal theory in …

GENERALIZATIONS OF THE SIMPLE TORSION CLASS AND THE SPLITTING
PROPERTIES Page 1 Can. J. Math., Vol. XXVII, No. 5, 1975, pp. 1056-1074 …

T (M)=(x= M| Hom,(Ra, I (R))= 0) where I (R) is the injective hull of R as a left R-module. A left
R-module M is said to be torsion free if T (M)= 0. For the properties of torsion free modules …

Rings whose modules form few torsion classes Page 1 BULL. AUSTRAL. MATH. SOC. MOS
I8E40, I6A64, I6A2I VOL. 4 (1971), 355-359. Rings whose modules form few torsion classes …

Throughout this paper R will be a commutative ring with one, and all R-modules will be
unitary. Our purpose is to study commutative ring exten-sions S of R. As a key tool in our …

It is well known that a ring homomorphism 7: RS canonically defines a function 7, from R-tors
to S-tors which assigns to each torsion thlexy r on R-Mod the torsion theory a= 7,(r) defined …

When we consider modules A over a ring R which is not a commutative integral domain, the
usual torsion theory becomes somewhat inadequate, since zero-divisors of R are …

In a celebrated theorem, AW Goldie determined necessary and sufficient conditions that a
ring have a left quotient ring which is semisimple with minimum condition [4]. Our first main …