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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Higher relative primitive ideals
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by Guangfeng Jiang and Aron Simis PDF
Proc. Amer. Math. Soc. 129 (2001), 647-655 Request permission

Abstract:

The main object of this note is to introduce a higher order analog of the so-called primitive ideal of $Y$ relative to $X$ introduced by Jiang–Pellikaan–Siersma, where $X\supset Y$ are germs of analytic subspaces of $(\mathbb {C}^n,0)$. Our treatment of the problem is ideal-theoretic throughout, using the notion of iterated higher differential operators. Some examples from singularity theory are worked out. We establish the connection between higher primitive ideals and (relative) symbolic powers of an ideal and give an effective algorithm to compute both.
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Additional Information
  • Guangfeng Jiang
  • Affiliation: Department of Mathematics, Jinzhou Normal University, Jinzhou City, Liaoning 121000, People’s Republic of China
  • Aron Simis
  • Affiliation: Departamento de Matemática, CCEN, Universidade Federal de Pernambuco, Av. Prof. Luis Freire, 50740-540 Recife, PE, Brazil
  • MR Author ID: 162400
  • Email: aron@dmat.ufpe.br
  • Received by editor(s): March 18, 1999
  • Received by editor(s) in revised form: May 12, 1999
  • Published electronically: September 19, 2000
  • Additional Notes: The first author was supported by JSPS: P98028, and the second author was partially supported by CNPq, Brazil.
  • Communicated by: Wolmer V. Vasconcelos
  • © Copyright 2000 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 129 (2001), 647-655
  • MSC (2000): Primary 13N15, 14B05; Secondary 13N10, 13P99, 16S32, 32S05
  • DOI: https://doi.org/10.1090/S0002-9939-00-05597-0
  • MathSciNet review: 1707149