Primary decomposition II: Primary components and linear growth
نویسندگان
چکیده
منابع مشابه
Primary Decomposition Ii: Primary Components and Linear Growth
We study the following properties about primary decomposition over a Noetherian ring R: (1) For finitely generated modules N ⊆ M and a given subset X = {P1, P2, . . . , Pr} ⊆ Ass(M/N), we define an X-primary component of N ( M to be an intersection Q1 ∩ Q2 ∩ · · · ∩ Qr for some Pi-primary components Qi of N ⊆ M and we study the maximal X-primary components of N ⊆ M ; (2) We give a proof of the ...
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For finitely generated modules N ( M over a Noetherian ring R, we study the following properties about primary decomposition: (1) The Compatibility property, which says that if Ass(M/N) = {P1, P2, . . . , Ps} and Qi is a Pi-primary component of N ( M for each i = 1, 2, . . . , s, then N = Q1 ∩Q2 ∩ · · · ∩Qs; (2) For a given subset X = {P1, P2, . . . , Pr} ⊆ Ass(M/N), X is an open subset of Ass(...
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In this paper we investigate decompositions of submodules in modules over a Proufer domain into intersections of quasi-primary and classical quasi-primary submodules. In particular, existence and uniqueness of quasi-primary decompositions in modules over a Proufer domain of finite character are proved. Proufer domain; primary submodule; quasi-primary submodule; classical quasi-primary; decompo...
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These notes are an attempt to unify the presentations of associated primes and primary decomposition given by Atiyah-Macdonald [1], Bourbaki [2], and Matsumura [3]. Their definitions differ somewhat, and we hope that the ways in which we have chosen to highlight these differences will lead to the reader having a greater understanding of the important concepts described herein. The differing def...
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ژورنال
عنوان ژورنال: Journal of Pure and Applied Algebra
سال: 2006
ISSN: 0022-4049
DOI: 10.1016/j.jpaa.2005.07.004