A Weaker Form of Baer's Splitting Problem Over Valuation Domains

Weak Baer modules over graded rings

“…In [2], Fuchs and Viljoen introduced and classified the B * -modules for a valuation ring R: an R-module M is a B * -module if Ext 1 R (M, X) = 0 for each divisible module X and each torsion module X with bounded order. The concept of a B * -module was extended to the setting of a torsion theory over an associative ring in [14].…”

A weaker form of Baer’s splitting problem for torsion theories

“…In studying H*-modules, Fuchs and Viljoen [6] effectively separate out the D*modules for the usual torsion theory over a valuation domain as those modules B with pd H B $C 1. In this section we give a general characterization of F)*-modules for arbitrary torsion theories over any ring with T(R) = 0.…”

“…Following the notation of [6], we say that a module B is a B* -module if Ext/*(H,A) = 0 for each r-divisible X and each X with r-bounded order. In [6], B*-modules were studied for the usual torsion theory over a valuation domain. The motivation for studying 1?…”

“…The motivation for studying 1? *-modules in [6] comes from the study of Baer modules over commutative integral domains. The purpose of this paper is to initiate the study of B*-modules for torsion theories over more general rings.…”

Weak baer modules localized with respect to a torsion theory

“…(Received September 1, 1995) In [1], Fuchs and Viljoen described the modules B over a valuation domain R such that Ext R (B, X) = 0 for all bounded torsion and all divisible modules X. This weak form of Baer's splitting problem was considered in [4], [5], [6], and [7] for arbitrary torsion theories over an associative ring.…”