Article

On the Krull intersection theorem in function algebras

Published in: Quaestiones Mathematicae
Volume 40 , issue 3 , 2017 , pages: 363–380

DOI: 10.2989/16073606.2017.1289482

Author(s): Raymond Mortini Université de Lorraine, France , Rudolf Rupp Fakultät für Angewandte Mathematik, Physik und Allgemeinwissenschaften, Germany , Amol Sasane Department of Mathematics, United Kingdom

Keywords: Primary: 46E25 , Secondary: 13A15 , 13G05 , 46J15 , Primary: 46E25 , Secondary: 13A15 , 13G05 , 46J15

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Abstract

A version of the Krull intersection theorem states that for Noetherian integral domains the Krull intersection ki(I) of every proper ideal I is trivial; that is We investigate the validity of this result for various function algebras R, present ideals I of R for which ki(I) ≠ {0}, and give conditions on I so that ki(I) = {0}.

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