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On the ring of locally bounded Nash meromorphic functions

Published online by Cambridge University Press:  17 April 2009

Wojciech Kucharz  and
Kamil Rusek
Wojciech Kucharz
Affiliation:
Department of Mathematics and Statistics, University of New Mexico, Albuquerque NM 87131, United States of America, e-mail: [email protected]
Kamil Rusek
Affiliation:
Institute of Mathematics, Jagiellonian University, Reymonta 4, 30–059 Kraków, Poland, e-mail: [email protected]
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Abstract

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We show that the ring of locally bounded Nash meromorphic functions on a connected d-dimensional Nash submanifold of ℝn is a Prüfer domain and every finitely generated ideal in this ring can be generated by d + 1 elements.

Moreover, every finitely generated ideal can be generated by d elements if and only if the Nash manifold is noncompact.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 54 , Issue 3 , December 1996 , pp. 503 - 507
Copyright
Copyright © Australian Mathematical Society 1996

References

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