All n-cotilting modules are pure-injective

We prove that all n-cotilting R-modules are pure-injective for any ring R and any n \ge 0. To achieve this, we prove that {^{\perp_1} U} is a covering class whenever U is an R-module such that {^{\perp_1} U} is closed under products and pure submodules.

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Bibliographic Details
Published in:Proceedings of the American Mathematical Society 2006-07, Vol.134 (7), p.1891-1897
Main Author: SOVICEK, Jan
Format: Article
Language:English
Subjects:
Algebra
Associative rings and algebras
Cardinality
Exact sciences and technology
Homomorphisms
Induction assumption
Logic and foundations
Mathematical completeness
Mathematical logic, foundations, set theory
Mathematical rings
Mathematics
Sciences and techniques of general use
Set theory
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Description
Summary:We prove that all n-cotilting R-modules are pure-injective for any ring R and any n \ge 0. To achieve this, we prove that {^{\perp_1} U} is a covering class whenever U is an R-module such that {^{\perp_1} U} is closed under products and pure submodules.
ISSN:0002-9939
1088-6826
DOI:10.1090/S0002-9939-06-08256-6