Weak baer modules localized with respect to a torsion theory
Weak Krull-Schmidt for Infinite Direct Sums of Cyclically Presented Modules over Local Rings
Weak Krull-Schmidt theorem
Recently, A. Facchini [3] showed that the classical Krull-Schmidt theorem fails for serial modules of finite Goldie dimension and he proved a weak version of this theorem within this class. In this remark we shall build this theory axiomatically and then we apply the results obtained to a class of some modules that are torsionfree with respect to a given hereditary torsion theory. As a special case we obtain that the weak Krull-Schmidt theorem holds for the class of modules that are both uniform...
Weak multiplication modules over a pullback of Dedekind domains
Let R be the pullback, in the sense of Levy [J. Algebra 71 (1981)], of two local Dedekind domains. We classify all those indecomposable weak multiplication R-modules M with finite-dimensional top, that is, such that M/Rad(R)M is finite-dimensional over R/Rad(R). We also establish a connection between the weak multiplication modules and the pure-injective modules over such domains.
Weak -injective and weak -fat modules
We introduce and study the concepts of weak -injective and weak -flat modules in terms of super finitely presented modules whose projective dimension is at most , which generalize the -FP-injective and -flat modules. We show that the class of all weak -injective -modules is injectively resolving, whereas that of weak -flat right -modules is projectively resolving and the class of weak -injective (or weak -flat) modules together with its left (or right) orthogonal class forms a hereditary...
Weakly compact cardinals and -torsionless modules.
Weakly periodic and subweakly periodic rings.
Weakly regular modules over normal rings.
When does an AB5* module have finite hollow dimension?
Using a lattice-theoretical approach we find characterizations of modules with finite uniform dimension and of modules with finite hollow dimension.
When is a quasi-p-projective module discrete?
When is the category of flat modules abelian?
Let Fl(R) denote the category of flat right modules over an associative ring R. We find necessary and sufficient conditions for Fl(R) to be a Grothendieck category, in terms of properties of the ring R.
When the intrinsic algebraic entropy is not really intrinsic
The intrinsic algebraic entropy ent(ɸ) of an endomorphism ɸ of an Abelian group G can be computed using fully inert subgroups of ɸ-invariant sections of G, instead of the whole family of ɸ-inert subgroups. For a class of groups containing the groups of finite rank, aswell as those groupswhich are trajectories of finitely generated subgroups, it is proved that only fully inert subgroups of the group itself are needed to comput ent(ɸ). Examples show how the situation may be quite different outside...
Whitehead property of modules
Wild Hereditary Artin Algebras and Linear Methods.
Wild tilted algebras revisited