query: Primary decomposition in Noetherian rings
positive_passages.docid: 148208
positive_passages.text: In Noetherian ring $R$, ideal $I\subset R$, $P\in\mathrm{Ass}(I),P=I:a$ for some $a\in R$.
negative_passages.docid: 29981
negative_passages.text: Why are Noetherian Rings important?
negative_passages.docid: 108767
negative_passages.text: Irreducible Components of the Prime Spectrum of a Quotient Ring and Primary Decomposition
negative_passages.docid: 93670
negative_passages.text: A surjective endomorphism (of a Noetherian ring) is injective.
negative_passages.docid: 138882
negative_passages.text: A prime poset of ideals
negative_passages.docid: 1425
negative_passages.text: The Chinese Remainder Theorem for Rings.
negative_passages.docid: 52602
negative_passages.text: $K[X^2,X^3]\subset K[X]$ is a Noetherian domain and all its prime ideals are maximal
negative_passages.docid: 67706
negative_passages.text: If $R$ is a Noetherian ring then $R[[x]]$ is also Noetherian
negative_passages.docid: 154530
negative_passages.text: Rings whose elements are partitioned between units and zero-divisors.
negative_passages.docid: 31585
negative_passages.text: Primary ideals of $\mathbb{Z}$
negative_passages.docid: 92822
negative_passages.text: Finite number of elements generating the unit ideal of a commutative ring
negative_passages.docid: 153210
negative_passages.text: Why is every Noetherian zero-dimensional scheme finite discrete?
negative_passages.docid: 105913
negative_passages.text: Calculations in quotient rings
negative_passages.docid: 39576
negative_passages.text: Quotient ring being isomorphic to the initial ring
negative_passages.docid: 74314
negative_passages.text: Noetherian ring and the same prime divisors
negative_passages.docid: 28518
negative_passages.text: Hom of finitely generated modules over a noetherian ring
negative_passages.docid: 50828
negative_passages.text: Weil divisors on normal Noetherian schemes