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On ideals of minors of matrices with indeterminate entries

Katzman, M. (2005) On ideals of minors of matrices with indeterminate entries. Communications in Algebra, 36 (1). pp. 104-111. ISSN 0092-7872

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This paper has two aims. The first is to study ideals of minors of matrices whose entries are among the variables of a polynomial ring. Specifically, we describe matrices whose ideals of minors of a given size are prime. The main result in the first part of this paper is a theorem which gives sufficient conditions for the ideal of minors of a matrix to be prime. This theorem is general enough to include interesting examples, such as the ideal of maximal minors of catalecticant matrices and their generalisations discussed in the second part of the paper. The second aim of this paper is to settle a specific problem raised by David Eisenbud and Frank-Olaf Schreyer on the primary decomposition of an ideal of maximal minors. We solve this problem by applying the theorem above together with some ad-hoc techniques.

Item Type: Article
Copyright, Publisher and Additional Information: © 2008 Taylor and Francis. This is an author produced version of a paper subsequently published in Communications in Algebra. Uploaded in accordance with the publisher's self-archiving policy.
Keywords: determinantal ideals
Institution: The University of Sheffield
Academic Units: The University of Sheffield > Faculty of Science (Sheffield) > School of Mathematics and Statistics (Sheffield)
Depositing User: Miss Anthea Tucker
Date Deposited: 19 Nov 2009 14:45
Last Modified: 16 Nov 2015 11:48
Published Version: http://dx.doi.org/10.1080/00927870701665206
Status: Published
Publisher: Taylor & Francis
Identification Number: 10.1080/00927870701665206
URI: http://eprints.whiterose.ac.uk/id/eprint/10164

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