JP Journal of Algebra, Number Theory and Applications
Volume 14, Issue 2, Pages 211 - 220
(August 2009)
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CLASSIFYING SUBCATEGORIES OF MODULES OVER A PID
Sunil K. Chebolu (Canada)
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of R-modules is triangulated if whenever two terms of a short
triangulated sequence belong to
then so does the
third term. In this note, we give a classification of triangulated subcategories
of finitely generated modules over a principal ideal domain. As a corollary, we
show that in the category of finitely generated modules over a PID, thick
subcategories (triangulated subcategories closed under direct summands), wide
subcategories (abelian subcategories closed under extensions) and Serre
subcategories (wide subcategories closed under kernels) coincide and correspond
to specialisation closed subsets of Spec (R).