A note on indecomposable modules over valuation domains
A simple proof of uniqueness for torsion modules over principal ideal domains.
The aim of this note is to give an alternative proof of uniqueness for the decomposition of a finitely generated torsion module over a P.I.D. (= principal ideal domain) as a direct sum of indecomposable submodules.Our proof tries to mimic as far as we can the standard procedures used when dealing with vector spaces.For the sake of completeness we also include a proof of the existence theorem.
A Theorem of Grothendieck Using Picard Groups for the Algebraist.
Arbitrarily large indecomposable divisible torsion modules over certain valuation domains
Cotangent Functors of Curve Singularities.
Cotorsion modules for torsion theories
Invariants for quasi-injective modules over valuation domains
Quasi-injective modules over valuation domains are classified by means of complete sets of cardinal invariants.
Kaplansky classes
Large indecomposable modules in torsion theories.
Modules of finite projective dimension with negative intersection multiplicities.
On a non-vanishing Ext
On the ring of quotients of a noetherian commutative ring with respect to the Dickson topology
On torsion Gorenstein injective modules
In this paper, we define Gorenstein injective rings, Gorenstein injective modules and their envelopes. The main topic of this paper is to show that if is a Gorenstein integral domain and is a left -module, then the torsion submodule of Gorenstein injective envelope of is also Gorenstein injective. We can also show that if is a torsion -module of a Gorenstein injective integral domain , then the Gorenstein injective envelope of is torsion.
Primary decomposition of torsion -modules.
Quasi-seperable und koseperable Moduln über diskreten Bewertungsringen.
Rank-two torsion-free modules over valuation domains
Regular submodules of torsion modules over a discrete valuation domain
A submodule of a -primary module of bounded order is known to be regular if and have simultaneous bases. In this paper we derive necessary and sufficient conditions for regularity of a submodule.
Relative multiplication and distributive modules
We study the construction of new multiplication modules relative to a torsion theory . As a consequence, -finitely generated modules over a Dedekind domain are completely determined. We relate the relative multiplication modules to the distributive ones.
Some properties of Butler modules over valuation domains
Sur les algebres de Rees II.