Premium
Derived Functors of Hom Relative to Flat Covers
Author(s) -
Aldrich Stephen T.,
Enochs Edgar E.,
Lopez Ramos Juan A.
Publication year - 2002
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/1522-2616(200207)242:1<17::aid-mana17>3.0.co;2-f
Subject(s) - mathematics , functor , dedekind cut , class (philosophy) , pure mathematics , ext functor , functor category , artificial intelligence , computer science
We study the derived functors of Hom that are computed by using flat resolutions of Hom. These are denoted $ \overline {Ext} $ n . We compare these with the usual Ext n 's and show that $ \overline {Ext} $ 1 ⊂ Ext 1 and indicate (using MacLane's terminology) why the class of associated short exact sequences is a proper class. When the ring is a Dedekind domain we classify the N such that $ \overline {Ext} $ n (–, N ) = 0 and show that unlike the situation for other classically defined right derived functors of Hom, Hom is not balanced relative to the two classes of modules that make $ \overline {Ext} $ 1 vanish.