Warfield Invariants in Abelian Group Algebras
Warfield invariants in abelian group rings.
Let R be a perfect commutative unital ring without zero divisors of char(R) = p and let G be a multiplicative abelian group. Then the Warfield p-invariants of the normed unit group V (RG) are computed only in terms of R and G. These cardinal-to-ordinal functions, combined with the Ulm-Kaplansky p-invariants, completely determine the structure of V (RG) whenever G is a Warfield p-mixed group.
Weak baer modules localized with respect to a torsion theory
Weak Baer modules over graded rings
In [2], Fuchs and Viljoen introduced and classified the -modules for a valuation ring R: an R-module M is a -module if for each divisible module X and each torsion module X with bounded order. The concept of a -module was extended to the setting of a torsion theory over an associative ring in [14]. In the present paper, we use categorical methods to investigate the -modules for a group graded ring. Our most complete result (Theorem 4.10) characterizes -modules for a strongly graded ring R...
Weak dimensions and Gorenstein weak dimensions of group rings
Let be a field, and let be a group. In the present paper, we investigate when the group ring has finite weak dimension and finite Gorenstein weak dimension. We give some analogous versions of Serre’s theorem for the weak dimension and the Gorenstein weak dimension.
Weak incidence algebra and maximal ring of quotients.
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 Polynomial Identities for M1,1(E)
* Partially supported by Universita` di Bari: progetto “Strutture algebriche, geometriche e descrizione degli invarianti ad esse associate”.We compute the cocharacter sequence and generators of the ideal of the weak polynomial identities of the superalgebra M1,1 (E).
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.
Whitehead Modules over Domains.
Wreath products in modular group algebras of some finite 2-groups.
Wreath products in the unit group of modular group algebras of 2-groups of maximal class.