97 citations · 128 across the 6 of their papers we have counts for
8 papers
Whitehead's problem and condensed mathematics
Jeffrey Bergfalk, Chris Lambie-Hanson, Jan Šaroch
One of the better-known independence results in general mathematics is Shelah's solution to Whitehead's problem of whether implies that an abelian…
Deconstructible abstract elementary classes of modules and categoricity
Jan Šaroch, Jan Trlifaj
We prove a version of Shelah's Categoricity Conjecture for arbitrary deconstructible classes of modules. Moreover, we show that if is a deconstructible class of modul…
The cotorsion pair generated by the Gorenstein projective modules and -pure-injective modules
Manuel Cortés-Izurdiaga, Jan Šaroch
We prove that, if is the class of all Gorenstein projective modules over a ring , then is a cotorsion pair…
Finitistic Dimension Conjectures via Gorenstein Projective Dimension
Pooyan Moradifar, Jan Šaroch
It is a well-known result of Auslander and Reiten that contravariant finiteness of the class (of finitely generated modules of finite projective…
Singular compactness and definability for -cotorsion and Gorenstein modules
Jan Šaroch, Jan Šťovíček
We introduce a general version of singular compactness theorem which makes it possible to show that being a -cotorsion module is a property of the complete theory of the module.…
Approximations and Mittag-Leffler conditions --- the applications
Lidia Angeleri Hügel, Jan Šaroch, Jan Trlifaj
A classic result by Bass says that the class of all projective modules is covering, if and only if it is closed under direct limits. Enochs extended the if-part by showing that eve…
Quasi-Euclidean subrings of Q[x]
Petr Glivický, Jan Šaroch
Using a nonstandard model of Peano arithmetic, we show that there are quasi-Euclidean subrings of Q[x] which are not k-stage Euclidean for any norm and positive integer k. These su…
The countable Telescope Conjecture for module categories
Jan Saroch, Jan Stovicek
By the Telescope Conjecture for Module Categories, we mean the following claim: "Let R be any ring and (A, B) be a hereditary cotorsion pair in Mod-R with A and B closed under dire…