TL;DR
This paper establishes the existence and uniqueness of coprimary filtrations for modules over Noetherian rings and coherent sheaves over locally Noetherian schemes, expanding foundational tools in commutative algebra.
Contribution
It proves the existence and uniqueness of coprimary filtrations for modules and coherent sheaves, including cases beyond finitely generated modules.
Findings
Proves existence of coprimary filtrations for modules over Noetherian rings.
Establishes uniqueness of these filtrations.
Extends the theory to coherent sheaves over schemes.
Abstract
The coprimary filtration is a basic construction in commutative algebra. In this article, we prove the existence and uniqueness of coprimary filtration of modules (not necessarily finitely generated) over a Noetherian ring. Moreover, we also prove the existence and uniqueness of coprimary filtrations of coherent sheaves over a locally Noetherian scheme.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Commutative Algebra and Its Applications · Algebraic Geometry and Number Theory