Higher relative primitive ideals

Authors:
Guangfeng Jiang and Aron Simis

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

Published electronically:
September 19, 2000

MathSciNet review:
1707149

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Abstract | References | Similar Articles | Additional Information

Abstract: The main object of this note is to introduce a higher order analog of the so-called primitive ideal of relative to introduced by Jiang-Pellikaan-Siersma, where are germs of analytic subspaces of . 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

Email:
aron@dmat.ufpe.br

DOI:
https://doi.org/10.1090/S0002-9939-00-05597-0

Keywords:
Primitive ideal,
symbolic power,
differential operator,
Jacobian matrix,
surface singularity

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

Article copyright:
© Copyright 2000
American Mathematical Society