Artinianess of graded local cohomology modules

Author:
Reza Sazeedeh

Journal:
Proc. Amer. Math. Soc. **135** (2007), 2339-2345

MSC (2000):
Primary 13D45, 13E10

Published electronically:
March 21, 2007

MathSciNet review:
2302554

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Abstract | References | Similar Articles | Additional Information

Abstract: Let be a Noetherian homogeneous ring with local base ring and let be a finitely generated graded -module. Let be the largest integer such that is not Artinian. We will prove that are Artinian for all and there exists a polynomial of degree less than such that for all . Let be the first integer such that the local cohomology module is not cofinite. We will show that for all the graded module is Artinian.

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Additional Information

**Reza Sazeedeh**

Affiliation:
Department of Mathematics, Urmia University, Urmia, Iran –and– Institute for Studies in Theoretical Physics and Mathematics (IPM), Tehran, Iran

Email:
rsazeedeh@ipm.ir

DOI:
http://dx.doi.org/10.1090/S0002-9939-07-08794-1

Keywords:
Graded local cohomology,
Artinian module,
polynomial

Received by editor(s):
January 9, 2006

Received by editor(s) in revised form:
April 6, 2006

Published electronically:
March 21, 2007

Additional Notes:
This research was in part supported by a grant from IPM (No. 84130033)

Communicated by:
Bernd Ulrich

Article copyright:
© Copyright 2007
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication.