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We prove a generalization of the Flat Cover Conjecture by showing for any ring R that (1) each (right R-) module has a Ker Ext(−, C)-cover, for any class of pure-injective modules C, and that (2) each module has a Ker Tor(−, B)-cover, for any class of left R-modules B. For Dedekind domains, we describe Ker Ext(−, C) explicitly for any class of cotorsion(More)
We consider the Whitehead problem for principal ideal domains of large size. It is proved, in ZFC, that some p.i.d.'s of size ≥ ℵ 2 have non-free Whitehead modules even though they are not complete discrete valuation rings. A module M is a Whitehead module if Ext 1 R (M, R) = 0. The second author proved that the problem of whether every Whitehead Z-module(More)