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National Repository of Grey Literature 2 records found  Search took 0.00 seconds. 
Testing the projectivity of modules
 Matoušek, Cyril ; Šaroch, Jan (advisor) ; Žemlička, Jan (referee)
In this thesis, we study the problem of the existence of test modules for the projectivity. A right R-module is said to be a test module if it holds for every right R-module M that M is projective whenever T ∈ M⊥ . We show that test modules exist over right perfect rings, although their existence is not provable in ZFC in case of non-right perfect rings. In order to prove this, we use Shelah's uni- formization principle, which is independent of the axioms of ZFC. Furthermore, we show that test modules exist over rings of finite global dimension assuming the weak diamond principle, which is also independent of ZFC. 1
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Max rings
 Beneš, Daniel ; Žemlička, Jan (advisor) ; Šaroch, Jan (referee)
Topic of this thesis is max rings, which are the rings, whose nonzero modu- les have maximal submodules. At the begining we prove a characterization of commutative max rings as rings with T-nilpotent Jacobson radical and von Ne- umann regular factor ring of the Jacobson radical. Our next concern are group rings, where we describe all commutative group rings, that are max. These are the group rings, that are composed from a commutative max ring and an abelian torsion group, where is finitely many elements of order pn for p not invertible in the ring. Finally we use this characterization to construct noncommutative group rings, which are max but not perfect.
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