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Every Cotorsion‐Free Ring is an Endomorphism Ring
Author(s) -
Dugas Manfred,
Göbel Rüdiger
Publication year - 1982
Publication title -
proceedings of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.899
H-Index - 65
eISSN - 1460-244X
pISSN - 0024-6115
DOI - 10.1112/plms/s3-45.2.319
Subject(s) - mathematics , countable set , endomorphism , abelian group , endomorphism ring , pure mathematics , ring (chemistry) , axiom , torsion (gastropod) , discrete mathematics , combinatorics , geometry , medicine , chemistry , surgery , organic chemistry
Some years ago A. L. S. Corner proved that every countable and cotorsion‐free ring can be realized as the endomorphism ring of some torsion‐free abelian group. This result has many interesting consequences for abelian groups. Using a set‐theoretic axiom ∇ k ., which follows for instance from V = L , we can drop the countability condition in Corner's theorem.