query: Flatness of quotient rings
positive_passages.docid: 142699
positive_passages.text: Is $R/N(R)$ a faithfully flat $R$-module?
negative_passages.docid: 154530
negative_passages.text: Rings whose elements are partitioned between units and zero-divisors.
negative_passages.docid: 158311
negative_passages.text: What is the dimension of $R[[X]]$ where $R$ is a Noetherian ring?
negative_passages.docid: 62917
negative_passages.text: Associated Prime Ideals in a Noetherian Ring; Exercise 6.4 in Matsumura
negative_passages.docid: 42871
negative_passages.text: Quotient of a local regular ring
negative_passages.docid: 19838
negative_passages.text: Prove that in general the set of the right zero divisors is different from the set of left zero divisors in a ring R
negative_passages.docid: 79650
negative_passages.text: Division Rings and Division Algebras
negative_passages.docid: 105913
negative_passages.text: Calculations in quotient rings
negative_passages.docid: 143884
negative_passages.text: A non-noetherian ring with noetherian spectrum
negative_passages.docid: 77862
negative_passages.text: Question about fields and quotients of polynomial rings
negative_passages.docid: 129025
negative_passages.text: Quotient ring local if Ring is local
negative_passages.docid: 40996
negative_passages.text: Proving that free modules are flat (without appealing projective modules)
negative_passages.docid: 91294
negative_passages.text: order of quotient ring
negative_passages.docid: 129858
negative_passages.text: "Almost" ring homomorphism
negative_passages.docid: 26805
negative_passages.text: Non-Noetherian 0-dimensional ring
negative_passages.docid: 34183
negative_passages.text: An equivalent condition with $\{0\}$ being the only nilpotent ideal
negative_passages.docid: 39755
negative_passages.text: In a faithfully flat ring extension, is $\operatorname{ht}I=\operatorname{ht}IS$ right?