query: Finite extension of Noetherian rings
positive_passages.docid: 13901
positive_passages.text: Finitely many prime ideals lying over $\mathfrak{p}$
negative_passages.docid: 62917
negative_passages.text: Associated Prime Ideals in a Noetherian Ring; Exercise 6.4 in Matsumura
negative_passages.docid: 4397
negative_passages.text: Finite rings without zero divisors are division rings.
negative_passages.docid: 92822
negative_passages.text: Finite number of elements generating the unit ideal of a commutative ring
negative_passages.docid: 157499
negative_passages.text: Every finite extension of a finite field is separable
negative_passages.docid: 63736
negative_passages.text: Every radical ideal in a Noetherian ring is a finite intersection of primes
negative_passages.docid: 109034
negative_passages.text: Does a finite $[E:K]_s$ imply that $[E_s:K]$ is finite?
negative_passages.docid: 127419
negative_passages.text: Subspace of Noetherian space still Noetherian
negative_passages.docid: 48009
negative_passages.text: Left inverse implies right inverse in a finite ring
negative_passages.docid: 140553
negative_passages.text: An ideal which is not finitely generated
negative_passages.docid: 7645
negative_passages.text: Noetherian property for exact sequence
negative_passages.docid: 116526
negative_passages.text: Finite ring has only zero divisors and units
negative_passages.docid: 79897
negative_passages.text: if R is a commutative ring in which all the prime ideals are finitely generated then R is Noetherian
negative_passages.docid: 28518
negative_passages.text: Hom of finitely generated modules over a noetherian ring
negative_passages.docid: 121008
negative_passages.text: A non-noetherian ring with all localizations noetherian
negative_passages.docid: 116000
negative_passages.text: Prove that prime ideals of a finite ring are maximal
negative_passages.docid: 59687
negative_passages.text: Suppose $M$ is a finitely generated module over $R$ where $R$ is a Noetherian ring. Prove that $M$ is a noetherian module.