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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Subcategories of extension modules by Serre subcategories


Author: Takeshi Yoshizawa
Journal: Proc. Amer. Math. Soc. 140 (2012), 2293-2305
MSC (2010): Primary 13C60, 13D45
Published electronically: November 23, 2011
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Abstract: In 1962, P. Gabriel showed the existence of a lattice isomorphism between the set of Serre subcategories of the category consisting of finitely generated modules and the set of specialization closed subsets of the set of prime ideals. In this paper, we consider subcategories consisting of the extensions of modules in two given Serre subcategories to find a method of constructing Serre subcategories of the category of modules. We shall give a criterion for this subcategory to be a Serre subcategory.


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Additional Information

Takeshi Yoshizawa
Affiliation: Graduate School of Natural Science and Technology, Okayama University, Okayama 700-8530, Japan
Email: tyoshiza@math.okayama-u.ac.jp

DOI: http://dx.doi.org/10.1090/S0002-9939-2011-11108-0
PII: S 0002-9939(2011)11108-0
Keywords: Extension module, local cohomology, Serre subcategory
Received by editor(s): November 1, 2010
Received by editor(s) in revised form: February 28, 2011
Published electronically: November 23, 2011
Communicated by: Irena Peeva
Article copyright: © Copyright 2011 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.