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pro vyhledávání: '"Trlifaj, Jan"'
We strengthen a result of Bagaria and Magidor~\cite{MR3152715} about the relationship between large cardinals and torsion classes of abelian groups, and prove that (1) the \emph{Maximum Deconstructibility} principle introduced in \cite{Cox_MaxDecon}
Externí odkaz:
http://arxiv.org/abs/2406.02829
Autor:
Yassine, Asmae Ben, Trlifaj, Jan
The approximation classes of modules that arise as components of cotorsion pairs are tied up by Salce's duality. Here we consider general approximation classes of modules and investigate possibilities of dualization in dependence on closure propertie
Externí odkaz:
http://arxiv.org/abs/2401.11979
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:
Trlifaj, Jan
Assume that $R$ is a non-right perfect ring. Then there is a proper class of classes of (right $R$-) modules closed under transfinite extensions lying between the classes $\mathcal P _0$ of projective modules, and $\mathcal F _0$ of flat modules. The
Externí odkaz:
http://arxiv.org/abs/2303.12549
Autor:
Trlifaj, Jan
Publikováno v:
Proc. Amer. Math. Soc. Ser. B 10(2023), pp. 369-381
For each deconstructible class of modules $\mathcal D$, we prove that the categoricity of $\mathcal D$ in a big cardinal is equivalent to its categoricity in a tail of cardinals. We also prove Shelah's Categoricity Conjecture for $(\mathcal D, \prec)
Externí odkaz:
http://arxiv.org/abs/2212.04433
Autor:
Yassine, Asmae Ben, Trlifaj, Jan
The ascent and descent of the Mittag-Leffler property were instrumental in proving Zariski locality of the notion of an (infinite dimensional) vector bundle by Raynaud and Gruson in \cite{RG}. More recently, relative Mittag-Leffler modules were emplo
Externí odkaz:
http://arxiv.org/abs/2208.00869
Autor:
Trlifaj, Jan
Publikováno v:
J. Algebra 601(2022), 87-100
We apply set-theoretic methods to study projective modules and their generalizations over transfinite extensions of simple artinian rings R. We prove that if R is small, then the Weak Diamond implies that projectivity of an arbitrary module can be te
Externí odkaz:
http://arxiv.org/abs/2203.06005
Autor:
Ben Yassine, Asmae, Trlifaj, Jan
Publikováno v:
In Journal of Pure and Applied Algebra January 2025 229(1)
Autor:
Trlifaj, Jan
We apply set-theoretic methods to study projective modules and their generalizations over transfinite extensions of simple artinian rings R. When R is hereditary and of cardinality at most $2^\omega$, we prove that the Weak Diamond and CH imply that
Externí odkaz:
http://arxiv.org/abs/2112.09643