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Torsion-free Abelian groups torsion over their endomorphism rings

Published online by Cambridge University Press:  17 April 2009

Theodore G. Faticoni
Theodore G. Faticoni
Affiliation:
Department of MathematicsFordham University BronxNew York 10458United States of America
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Abstract

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We use a variation on a construction due to Corner 1965 to construct (Abelian) groups A that are torsion as modules over the ring End (A) of group endomorphisms of A. Some applications include the failure of the Baer-Kaplansky Theorem for Z[X]. There is a countable reduced torsion-free group A such that IA = A for each maximal ideal I in the countable commutative Noetherian integral domain, End (A). Also, there is a countable integral domain R and a countable. R-module A such that (1) R = End(A), (2) T0 ⊗RA ≠ 0 for each nonzero finitely generated (respectively finitely presented) R-module T0, but (3) T ⊗RA = 0 for some nonzero (respectively nonzero finitely generated). R-module T.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 50 , Issue 2 , October 1994 , pp. 177 - 195
Copyright
Copyright © Australian Mathematical Society 1994

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