Weak diamond, weak projectivity, and transfinite extensions of simple artinian rings

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 tested at the layer epimorphisms of R.

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Bibliographic Details
Published inarXiv.org
Main Author Trlifaj, Jan
Format Paper Journal Article
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 11.03.2022
Subjects
Diamonds
Mathematics - Logic
Mathematics - Representation Theory
Mathematics - Rings and Algebras
Modules
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Summary: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 tested at the layer epimorphisms of R.
ISSN:2331-8422
DOI:10.48550/arxiv.2203.06005