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On the lattice of right ideals of the endomorphism ring of an abelian group

Published online by Cambridge University Press:  17 April 2009

Theodore G. Faticoni
Theodore G. Faticoni
Affiliation:
Department of Mathematics, Fordham University, Bronx NY. 10458, United States of America.
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Abstract

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Let A be an abelian group, let ∧ = End (A), and assume that A is a flat left ∧-module. Then σ = { right ideals I ⊂ ∧ | IA = A} generates a linear topology oil ∧. We prove that Hom(A,·) is an equivalence from the category of those groups B ⊂ An satisfying B = Hom(A, B)A, onto the category of σ-closed submodules of finitely generated free right ∧-modules. Applications classify the right ideal structure of A, and classify torsion-free groups A of finite rank which are (nearly) isomorphic to each A-generated subgroup of finite index in A.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 38 , Issue 2 , October 1988 , pp. 273 - 291
Copyright
Copyright © Australian Mathematical Society 1988

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