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Full-Text Articles in Algebra
Closure Under Transfinite Extensions, Edgar E. Enochs, Alina Iacob, Overtoun Jenda
Closure Under Transfinite Extensions, Edgar E. Enochs, Alina Iacob, Overtoun Jenda
Alina Iacob
The closure under extensions of a class of objects in an abelian category is often an important property of that class. Recently the closure of such classes under transfinite extensions (both direct and inverse) has begun to play an important role in several areas of mathematics, for example in Quillen’s theory of model categories and in the theory of cotorsion pairs. In this paper we prove that several important classes are closed under transfinite extensions
Closure Under Transfinite Extensions, Edgar E. Enochs, Alina Iacob, Overtoun Jenda
Closure Under Transfinite Extensions, Edgar E. Enochs, Alina Iacob, Overtoun Jenda
Alina Iacob
The closure under extensions of a class of objects in an abelian category is often an important property of that class. Recently the closure of such classes under transfinite extensions (both direct and inverse) has begun to play an important role in several areas of mathematics, for example, in Quillen's theory of model categories and in the theory of cotorsion pairs. In this paper we prove that several important classes are closed under transfinite extensions.
Balance In Generalized Tate Cohomology, Alina Iacob
Balance In Generalized Tate Cohomology, Alina Iacob
Balance In Generalized Tate Cohomology, Alina Iacob
Alina Iacob
We consider two preenveloping classes of left R-modules ℐ, ℰ such that Inj ⊂ ℐ ⊂ ℰ, and a left R-module N. For any left R-module M and n ≥ 1 we define the relative extension modules (M, N) and prove the existence of an exact sequence connecting these modules and the modules (M, N) and (M, N). We show that there is a long exact sequence of (M, −) associated with a Hom(−, ℰ) exact sequence 0 → N′ → N → N′′ → 0 and a long exact sequence of (−, N) associated with a Hom(−, ℰ) exact …