On Torsion-free Modules over Valuation Domains
In this survey article, we indicate how some of the recent ideas and techniques introduced in the study of infinite rank Butler groups can be successfully used in the investigation of the homological dimensions of torsion-free modules over integral domains and, in particular, over valuation domains.
KeywordsExact Sequence Direct Summand Integral Domain Projective Dimension Torsion Theory
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- D. Arnold and C. Vinsonhaler, Pure subgroups of finite rank completely decomposable groups II, Lecture Notes in Math. 1006, Springer-Verlag, Heidelberg, New York (1983), 97–143.Google Scholar
- L. Fuchs and K. M. Rangaswamy, On the global balanced-projective dimension of valuation domains, Periodica Math. Hungarica, to appear.Google Scholar
- L. Fuchs and L. Salce, Modules over Valuation Domains, Lecture Notes in Pure and Applied Math. 97 Marcel-Dekker, New York, 1985.Google Scholar
- L. Nongxa, K. M. Rangaswamy and C. Vinsonhaler, Torsion-free modules of finite balanced-projective dimension over valuation domains, J. Pure and Applied Algebra, to appear.Google Scholar