Let R be a commutative integral domain with 1 and Q its field of quotients. We show that if p.d.$\sb{\rm R}$ Q = 1, then Q/R is a direct sum of countably generated R-modules. We also show that any divisible torsion module of projective dimension one over R with p.d.$\sb{\rm R}$ Q = 1 is a direct sum of countably generated R-modules. These give us two characterizations of domains R with p.d.$\sb{\rm R}$ Q = 1. We find a classification theorem of divisible modules of projective dimension one over R with p.d.$\sb{\rm R}$ Q = 1. We show that countably generated torsion-free modules over valuation domains R with p.d.$\sb{\rm R}$ Q $>$ 1 can be embedded in free R-modules and generalize this to uncountably generated torsion-free modules / acase@tulane.edu
| Identifer | oai:union.ndltd.org:TULANE/oai:http://digitallibrary.tulane.edu/:tulane_26710 |
| Date | January 1988 |
| Contributors | Lee, Sang Bum (Author), Fuchs, Laszlo (Thesis advisor) |
| Publisher | Tulane University |
| Source Sets | Tulane University |
| Language | English |
| Detected Language | English |
| Rights | Access requires a license to the Dissertations and Theses (ProQuest) database., Copyright is in accordance with U.S. Copyright law |
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