On the nontrivial solvability of systems of homogeneous linear equations over $\mathbb Z$ in ZFC

DOI10.14712/1213-7243.2020.017OpenAlexW3097064165MaRDI QIDQ5140418

Jan Šaroch

Publication date: 15 December 2020

Published in: Commentationes Mathematicae Universitatis Carolinae (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1812.06958

zbMATH Keywords

\(\kappa\)-free group\(\mathcal L_{\omega_1\omega}\)-compact cardinalhomogeneous \(\mathbb{Z}\)-linear equation

Mathematics Subject Classification ID

Projective and free modules and ideals in commutative rings (13C10) Consistency and independence results (03E35) Large cardinals (03E55) Automorphisms, homomorphisms, endomorphisms, etc. for abelian groups (20K30) Equational compactness (08A45)

Cites Work

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• Approximations and endomorphism algebras of modules. Volume 1: Approximations. Volume 2: Predictions.
• \(\aleph_n\)-free modules with trivial duals
• ON ${\omega _1}$-STRONGLY COMPACT CARDINALS
• Every Cotorsion-Free Ring is an Endomorphism Ring
• On the solvability of systems of linear equations over the ring $\mathbb{Z}$ of integers
• Group radicals and strongly compact cardinals

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