, Volume 150, Issue 1, pp 363-373

Baer modules over valuation domains

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Summary

A module B over a commutative domain R is said to be a Baer module if Ext R 1 (B, T)=0for all torsion R-modules T. The case in which R is an arbitrary valuation domain is investigated, and it is shown that in this case Baer modules are necessarily free. The method employed is totally different from Griffith's method for R=Z which breaks down for non-hereditary rings.

This research was partially supported by NSF Grants DMS-8400451 and DMS-8500933.