منابع مشابه
On the Cogeneration of Cotorsion Pairs
Let R be a Dedekind domain. In [6], Enochs’ solution of the Flat Cover Conjecture was extended as follows: (∗) If C is a cotorsion pair generated by a class of cotorsion modules, then C is cogenerated by a set. We show that (∗) is the best result provable in ZFC in case R has a countable spectrum: the Uniformization Principle UP implies that C is not cogenerated by a set whenever C is a cotorsi...
متن کاملTilting Cotorsion Pairs
Let R be a ring and T be a 1-tilting right R-module. Then T is of countable type. Moreover, T is of finite type in case R is a Prüfer domain.
متن کاملNotes on Cotorsion Theories and Model Categories
These are notes for two talks given by Mark Hovey at the Summer School on the Interactions between Homotopy Theory and Algebra at the University of Chicago, July 26 to August 6, 2004. Because they are notes, they are a bit more chatty and a bit more likely to contain errors than a paper would be, so caveat lector. They are based on the papers [Hov02], [Gil04b], and [Gil04a], and concern the rel...
متن کاملOn n-Perfect Rings and Cotorsion Dimension
A ring is called n-perfect (n ≥ 0), if every flat module has projective dimension less or equal than n. In this paper, we show that the n-perfectness relate, via homological approach, some homological dimension of rings. We study n-perfectness in some known ring constructions. Finally, several examples of n-perfect rings satisfying special conditions are given.
متن کاملCotorsion Theories and Splitters
Let R be a subring of the rationals. We want to investigate self splitting R-modules G that is ExtR(G,G) = 0 holds and follow Schultz [22] to call such modules splitters. Free modules and torsion-free cotorsion modules are classical examples for splitters. Are there others? Answering an open problem by Schultz [22] we will show that there are more splitters, in fact we are able to prescribe the...
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ژورنال
عنوان ژورنال: Pacific Journal of Mathematics
سال: 1976
ISSN: 0030-8730,0030-8730
DOI: 10.2140/pjm.1976.62.163