… hereditary torsion theories in the category rWI of left i?-modules over a semiperfect ring R. …
in determining those hereditary torsion theories for which the torsion submodule is a direct …

… class is calléd a torsion theory. Sorne authors, notably Dickson [15] and Jans [20 J, have
called a pretorsion theory a torsion theory, and a torsion theory a hereditary torsion theory. Jans …

… torsion theory in the category R-Mod of left R-modules and the corresponding left Gabriel
topology N on R. The natural way to define relative semiperfect … '-semiperfect rings (that is, rings …

… We will show later that a ring R is -semiperfect if and only if … perfect ring is not necessarily
semiregular, a semiperfect ring … torsion theory, while what we gave in this paper is the setting …

… applications to torsion theory, as well as to an account of the basic theory of rings with various
… We have noticed that a semi-primary ring is both semi-perfect and semi-artinian. The class …

… For a general semiperfect ring, Acris(R) can have p-torsion, and the functor DR cannot be
expected to be fully faithful. The phenomenon that passing from Dieudonné modules to …

… Following Golan [GI], for the most part by a torsion theory 7 on the left R-modules we will
mean a hereditary torsion theory. We will use the term r-closed in place of r-pure, so N is a r-…

… a torsion theory. Kurata showed that there can be only our kinds of n-fold torsion theory. In this
… over a left and right perfect ring, the torsion theories being described in terms of properties …

… torsion theory is discussed and related to results of JP Jans. The rings, all of whose hereditary
torsion theories have … many right perfect rings, each of which has a unique maximal ideal. …

… Hence every torsionfree left module is torsionless, so that by Proposition 3.6 fRf is a
semiperfect ring. Also, by Lemma 3.4 every cocritical right module has a nonzero socle. Hence by …