… Here, given two modules A and X over a ring R, we say that a … modules which states that
a torsion-free extending module … assume that C is closed under isomorphisms or essential …

… of modules M over a ring R such that every submodule has a unique closure relative to a
hereditary torsion theory … We introduce two new module classes called τ-singular modules and …

… ; (2) the category of all left exact radicals on the category of left R-modules; (3) the category
of all hereditary torsion theories … integral closure and tight closure can be extended to unique …

… T and F can be (uniquely) extended to an idempotent comonad and monad, respectively. …
In Sections 4 and 5 we develop the second table. Torsion operators and torsion theories are …

… that the fine moduli space is unique up to isomorphism, if it … 4-torsion element whereas the
second one is only 2-torsion and … In this section k is an algebraically closed field, R a factorial, …

… closed and G = G L 2 ( F ) , the functor h matches up the simple nonsupersingular modules of
… Every module M in Mod ( R ) has a unique largest submodule t ( M ) which is contained in T …

… Lemma for Categories and torsion theories relative to Ext. … of isomorphisms (such an X is
unique up to isomorphism). The reader … We will always assume these clases are closed under …

… and torsion modules discussed in this paper are related, in … I-adically separated R-modules
is closed under products in R … The upper dotted vertical arrow is uniquely defined by the …

… of SE Dickson to torsion theories by two classes of modules is … closed classes of R-modules
and closed sets of left ideals of R. … Er(A) exists for every module A and is unique up to an …

… Goldie torsion modules and coprojectively generated by nonsingular … In the second part,
coprojective modules of this class which … f and the epimorphisms g uniquely up to isomorphism. …