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National Repository of Grey Literature 2 records found  Search took 0.02 seconds. 
Modules over string algebras
 Löwit, Jakub ; Šťovíček, Jan (advisor) ; Žemlička, Jan (referee)
The aim of this thesis is to investigate the categories of modules over the so called string algebras. In particular, we try to understand the cotorsion pairs in these categories, which boils down to understanding the decompositions of extensions of such modules. For string algebras with some oriented tree for the underlying quiver, we describe some classes given by these cotorsion pairs in terms of purely combinatorial closure properties. For any string algebras, the combinatorics appears to be similar, althought more complicated.
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Definable classes of modules and deconstruction of cotorsion pairs
 Dohnal, Garik ; Šaroch, Jan (advisor) ; Šťovíček, Jan (referee)
The goal of this work was to prove the fact, that definable closure of any subclass of cotorsion modules closed under direct sums consists of $\Sigma$-cotorsion modules. The only known proof uses substantially the calculus of derived category, in this work we tried to prove the same, but only by means of a given category of all right $R$-modules and set-theoretic properties of partial orders indexing direct systems of $R$-modules. The main results of this work are proved under additional assumptions on the ring $R$, in particular $\vert R\vert\leq\aleph_{\omega}$ or $\text{dim}(R)<\aleph_{\omega}$. Attempts to give s proof in the same general situation, where the fact is known to hold, was not successful. Powered by TCPDF (www.tcpdf.org)
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