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Endomorphism rings of Butler groups

Part of: Abelian groups

Published online by Cambridge University Press:  09 April 2009

D. M. Arnold  and
C. I. Vinsonhaler
D. M. Arnold
Affiliation:
Department of Mathematical SciencesNew Mexico State UniversityLas Cruces, New Mexico 88003, U.S.A.
C. I. Vinsonhaler
Affiliation:
Department of MathematicsUniversity of ConnecticutStorrs, Connecticut 06268, U.S.A.
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Abstract

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This note is devoted to the question of deciding whether or not a subring of a finite-dimensional algebra over the rationals, with additive group a Butler group, is the endomorphism ring of a Butler group (a Butler group is a pure subgroup of a finite direct sum of rank-1 torsion-free abelian groups). A complete answer is given for subrings of division algebras. Several applications are included.

MSC classification

Secondary: 20K15: Torsion-free groups, finite rank
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 42 , Issue 3 , June 1987 , pp. 322 - 329
Copyright
Copyright © Australian Mathematical Society 1987

References

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