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pro vyhledávání: '"Šaroch, Jan"'
One of the better-known independence results in general mathematics is Shelah's solution to Whitehead's problem of whether $\mathrm{Ext}^1(A,\mathbb{Z})=0$ implies that an abelian group $A$ is free. The point of departure for the present work is Clau
Externí odkaz:
http://arxiv.org/abs/2312.09122
Autor:
Šaroch, Jan, Trlifaj, Jan
We prove a version of Shelah's Categoricity Conjecture for arbitrary deconstructible classes of modules. Moreover, we show that if $\mathcal{A}$ is a deconstructible class of modules that fits in an abstract elementary class $(\mathcal{A},\preceq)$ s
Externí odkaz:
http://arxiv.org/abs/2312.02623
Autor:
Bazzoni, Silvana, Šaroch, Jan
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 verified, the conjecture remains open in its full generality. In this paper
Externí odkaz:
http://arxiv.org/abs/2303.08471
We show how to construct discretely ordered principal ideal subrings of $\mathbb Q[x]$ with various types of prime behaviour. Given any set $\mathcal D$ consisting of finite strictly increasing sequences $(d_1,d_2,\dots, d_l)$ of positive integers su
Externí odkaz:
http://arxiv.org/abs/2204.06866
Autor:
Šaroch, Jan
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 been verified, the conjecture remains open in its full generality. In thi
Externí odkaz:
http://arxiv.org/abs/2109.15016
Autor:
Cortés-Izurdiaga, Manuel, Šaroch, Jan
We prove that, if $\textrm{GProj}$ is the class of all Gorenstein projective modules over a ring $R$, then $\mathfrak{GP}=(\textrm{GProj},\textrm{GProj}^\perp)$ is a cotorsion pair. Moreover, $\mathfrak{GP}$ is complete when all projective modules ar
Externí odkaz:
http://arxiv.org/abs/2104.08602
Autor:
Moradifar, Pooyan, Šaroch, Jan
It is a well-known result of Auslander and Reiten that contravariant finiteness of the class $\mathcal{P}^{\mathrm{fin}}_\infty$ (of finitely generated modules of finite projective dimension) over an Artin algebra is a sufficient condition for validi
Externí odkaz:
http://arxiv.org/abs/2006.02182
Akademický článek
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Autor:
Šaroch, Jan, Trlifaj, Jan
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 generalizations and dualizations of factorization properties in dependence o
Externí odkaz:
http://arxiv.org/abs/1912.03749
Autor:
Šaroch, Jan
Inspired by a recent paper due to Jos\'{e} Luis Garc\'{i}a, we revisit the attempt of Daniel Simson to construct a counterexample to the pure semisimplicity conjecture. Using compactness, we show that the existence of such counterexample would readil
Externí odkaz:
http://arxiv.org/abs/1909.13864