Chase has given several characterizations of a right coherent ring, among which are: every
direct product of copies of the ring is left-flat; and every finitely generated submodule of a …

In this note we characterize those torsion theories over a semiperfect ring such that the class
of torsion free modules is closed under projective covers and the hereditary torsion theories …

Coherent rings relative to (hereditary) torsion theories have been studied in several papers.
The characterization, given by Cateforis I41, of nonsingular rings with flat maximal quotient …

Let R be any ring. We prove that every right R-module is coretractable if and only if R is right
perfect and every right R-module is small coretractable if and only if all torsion theories on R …

JP Jans has shown that if a ring R is right perfect, then a certain torsion in the category Mod
R of left R-modules is closed under taking direct products. Extending his method, JS Alin …

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 …

Hattori (1960) defined a right R-module A to be torsion-free if for all a∈ A and x∈ R, ax= 0
implies that there exist elements {x1, x2,…, xn}⊆ R with xix= 0 for all 1≦ i≦ n and {a1 …

Let R be a ring with identity. As in [I],[XI, and [= I, a class T of leftd (or right) R-modules is
called a torsion class if it is closed under direct sums, homomorphic images, and extensions …

ON A CLASS OF RATIONALLY COMPLETE RINGS Page 1 Quaestiones Mathematicae - 3(1978),
1-4 ON A CLASS OF RATIONALLY COMPLETE RINGS AR MEIJER ABSTRACT: Rings which …

Modules with Unique Closure Relative to a Torsion Theory Page 1 Canad. Math. Bull. Vol. 53
(2), 2010 pp. 230–238 doi:10.4153/CMB-2010-012-9 c©Canadian Mathematical Society 2009 …