Množinově-teoretické metody v teorii modulů

Šaroch, Jan

The thesis collects my actual contributions to the theory of cotorsion pairs, with closer attention paid to the application of set-theoretic methods in this area. It consists of an introduction and three papers with coauthors. The first two, already published, deal with the so-called Telescope Conjecture for Module Categories. We prove here, for instance, that a hereditary cotorsion pair (A, B) with the class B closed under direct limits is generated by a set of countably presented modules. Moreover, if the class A is closed under direct limits too, then the pair (A, B) is cogenerated by a set of indecomposable pure-injective modules. In the third paper, we deal with the cotorsion pairs which provide us with non-trivial examples of abstract elementary classes (in the sense of Shelah). Then we study the class D of all 1-projective modules, proving e.g. that-regardless of the ring-it always forms a Kaplansky class.

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