9 papers
Enochs Conjecture for cotorsion pairs and more
Silvana Bazzoni, Jan Šaroch
Enochs Conjecture asserts that each covering class of modules (over any ring) has to be closed under direct limits. Although various special cases of the conjecture have been verif…
Controlling distribution of prime sequences in discretely ordered principal ideal subrings of
Jana Glivická, Ester Sgallová, Jan Šaroch
We show how to construct discretely ordered principal ideal subrings of with various types of prime behaviour. Given any set consisting of finite strict…
Enochs' conjecture for small precovering classes of modules
Jan Šaroch
Enochs' conjecture asserts that each covering class of modules (over any fixed ring) has to be closed under direct limits. Although various special cases of the conjecture have bee…
Test sets for factorization properties of modules
Jan Šaroch, Jan Trlifaj
Baer's Criterion of injectivity implies that injectivity of a module is a factorization property w.r.t. a single monomorphism. Using the notion of a cotorsion pair, we study genera…
Pure semisimplicity conjecture and Artin problem for dimension sequences
Jan Šaroch
Inspired by a recent paper due to José Luis García, we revisit the attempt of Daniel Simson to construct a counterexample to the pure semisimplicity conjecture. Using compactness,…
On the nontrivial solvability of systems of homogeneous linear equations over in ZFC
Jan Šaroch
Following a recent paper by Herrlich and Tachtsis, we investigate in ZFC the following compactness question: for which unountable cardinals , an arbitrary nonempty system of…