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Higher relative primitive ideals
Author(s):
Guangfeng
Jiang;
Aron
Simis
Journal:
Proc. Amer. Math. Soc.
129
(2001),
647-655.
MSC (2000):
Primary 13N15, 14B05;
Secondary 13N10, 13P99, 16S32, 32S05
Posted:
September 19, 2000
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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.
References:
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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:
10.1090/S0002-9939-00-05597-0
PII:
S 0002-9939(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
Posted:
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 of article:
Copyright
2000,
American Mathematical Society
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