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Subcategories of extension modules by Serre subcategories
Author:
Takeshi Yoshizawa
Journal:
Proc. Amer. Math. Soc. 140 (2012), 2293-2305
MSC (2010):
Primary 13C60, 13D45
Posted:
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
Posted:
November 23, 2011
Communicated by:
Irena Peeva
Article copyright:
© Copyright 2011 American Mathematical Society
The copyright for this article reverts to public domain after
28 years from publication.
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