It is shown that, over suitable valuation domains R with field of quotients Q, the cotorsion
theory GK generated by K= Q/R coincides with the cotorsion theory C∂ cogenerated by the …

Publisher Summary This chapter provides an overview of the basic concepts of the Krull-
Schmidt theorem. The two proofs of the Krull-Schmidt-Azumaya theorem, mention …

Let. Z~ be a valuation domain and Q its" field of quotients. We denote by Yo (R) the class of
torsion-free R-modules of finite rank, and by the class of finitely generated torsion. R …

In that paper the notion of u-independence of units of a maximal immediate extension S of R
was used to construct two kinds of indecomposable finitely generated R-modules: uniform …

Sia R un anello commutativo. Due R-moduli si dicono quasi-isomorfise ciascuno è isomorfo
ad un sottomodulo dell'altro. Si prova che, a meno di quasi-isomorfismi, un R-modulo si …

In what follows, B will denote a valuation domain, ie a com-mutative domain with 1 in which
the ideals form a chain under inclusion. We assume that 1~ is not equal to its field Q of …

A note on indecomposable modules over valuation domains Page 1 RENDICONTI del
SEMINARIO MATEMATICO della UNIVERSITÀ DI PADOVA MATT D. LUNSFORD A note on …

We start the investigation of inert modules over valuation domains, a class of modules
containing finitely generated and quasi-injective modules. A complete description is …

Let R be a valuation domain. We say that a torsion-free R-module is minimal if it is
isomorphic to all its submodules of finite index. Here, the usual concept of finite index for …

We prove that a non linearly compact valuation domain R admits a proper immediate
extension S. This is the main point of Kaplansky's classical result that a valuation domain is …