We describe the torsion-free covers of cyclic modules, the pure-injective envelopes of ideals, the maximal immediate extensions of localizations and the injective envelopes of cyclics over valuation domains. We study the relations among these modules. This paper generalizes some results of Banaschewski, Cheatham, Enochs and Nishi. © 1985 The Weizmann Science Press of Israel.
Torsion-free covers and pure-injective envelopes over valuation domains
FACCHINI, ALBERTO
1985
Abstract
We describe the torsion-free covers of cyclic modules, the pure-injective envelopes of ideals, the maximal immediate extensions of localizations and the injective envelopes of cyclics over valuation domains. We study the relations among these modules. This paper generalizes some results of Banaschewski, Cheatham, Enochs and Nishi. © 1985 The Weizmann Science Press of Israel.
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