A note on ext-completions
نویسندگان
چکیده
منابع مشابه
A Note on Symmetry in the Vanishing of Ext
In [1] Avramov and Buchweitz proved that for finitely generated modules M and N over a complete intersection local ring R, Ext R (M, N) = 0 for all i ≫ 0 implies ExtiR(N, M) = 0 for all i ≫ 0. In this note we give some generalizations of this result. Indeed we prove the above mentioned result when (1) M is finitely generated and N is arbitrary, (2) M is arbitrary and N has finite length and (3)...
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The existence of valuation domains admitting non-standard uniserial modules for which certain Exts do not vanish was proved in [1] under Jensen’s Diamond Principle. In this note, the same is verified using the ZFC axioms alone. In the construction of large indecomposable divisible modules over certain valuation domainsR, the first author used the property thatR satisfied Ext1R(Q,U) 6= 0, where ...
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If A and B are Abelian groups, then Hom(A,B) is also an Abelian group under pointwise addition of functions. In this section we will see how Hom gives rise to classes of functors. Let A denote the category of Abelian groups. A covariant functor T : A → A associates to every Abelian group A an Abelian group T (A), and for every homomorphism f : A → B a homomorphism T (f) : T (A)→ T (B), such tha...
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Free regular and exact completions of categories with various ranks of weak limits are presented as subcategories of presheaf categories. Their universal properties can then be derived with standard techniques as used in duality theory.
متن کاملNotes on Tor and Ext
1. Basic homological algebra 1 1.1. Chain complexes 2 1.2. Maps and homotopies of maps of chain complexes 2 1.3. Tensor products of chain complexes 3 1.4. Short and long exact sequences 3 1.5. Dual cochain complexes and Hom complexes 4 1.6. Relations between ⊗ and Hom 4 2. The universal coefficient and Künneth theorems 5 2.1. Universal coefficients in homology 5 2.2. The Künneth theorem 6 2.3. ...
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ژورنال
عنوان ژورنال: Journal of Algebra
سال: 1971
ISSN: 0021-8693
DOI: 10.1016/0021-8693(71)90047-0