Free ideal rings (FIRs) introduced in (4) form a natural generalization of principal ideal
domains (PIDs), to which they reduce in the commutative case. However, they include many …

Recently, a proof of the existence of a flat cover of any module over an arbitrary associative
ring with unit has been finally given (see). In this paper we prove the existence of flat covers …

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

Suppose that R is a ring and that A is a chain complex over R. Inside the derived category of
differential graded R-modules there are naturally defined subcategories of A-torsion objects …

We revisit a construction of wide subcategories going back to work of Ingalls and Thomas.
To a torsion pair in the category $ R\operatorname {-}\operatorname {mod} $ of finitely …

*- Modules over ring extensions Page 1 COMMUNICATIONS IN ALGEBRA, 25(9), 2839-2860
(1997) *-Modules over Ring Extensions Kent R. Fuller Department of Mathematics University of …

We relate the theory of envelopes and covers to tilting and cotilting theory, for (infinitely
generated) modules over arbitrary rings. Our main result characterizes tilting torsion classes …

Let (F-,. F) be a hereditary torsion theory in a category Mod-R of unital right R-modules over
a ring R with identity 1 and 3'a reflective subcategory of Mod-R such that the left adjoint of …

A kernel functor (equivalently, a left exact torsion preradical) is a left exact subfunctor of the
identity on the category R-mod of left R-modules over a ring R with identity. A kernel functor …

The category of unital modules over a ring with identity element is characterized as a
cocomplete abelian category with a progenerator. More generally, every cocomplete abelian …