query: Is $R=K[\![x^3,x^2y,xy^2,y^3]\!]$ a Gorenstein ring?
positive_passages.docid: 25058
positive_passages.text: Is $R=K[|x^3,x^2y,xy^2,y^3|]$ a Gorenstein or a regular ring?
negative_passages.docid: 135699
negative_passages.text: Questions about a commutative ring with exactly three ideals
negative_passages.docid: 63568
negative_passages.text: Ring with finitely many zerodivisors
negative_passages.docid: 111104
negative_passages.text: Ring theory notation question
negative_passages.docid: 61292
negative_passages.text: How to know which elements are in the Quotient Ring $\mathbb{Z}[x]/\langle x, 2\rangle$?
negative_passages.docid: 21604
negative_passages.text: A complete ring with respect to an ideal
negative_passages.docid: 158311
negative_passages.text: What is the dimension of $R[[X]]$ where $R$ is a Noetherian ring?
negative_passages.docid: 115541
negative_passages.text: Subrings of polynomial rings over the complex plane
negative_passages.docid: 38817
negative_passages.text: Why is the ring of matrices over a field simple?
negative_passages.docid: 122012
negative_passages.text: The ideal $(x,y)$ is not a free $K[x,y]$-module
negative_passages.docid: 25764
negative_passages.text: Example of a ring such that $R^2\simeq R^3$, but $R\not\simeq R^2$ (as $R$-modules)
negative_passages.docid: 155642
negative_passages.text: Understanding divison by monic polynomial in $R[x]$ where $R$ is an arbitrary ring
negative_passages.docid: 69353
negative_passages.text: Show that a ring with only trivial right ideals is either a division ring or $|R|=p$ and $R^2=\{0\}$. Why would $R$ be finite?
negative_passages.docid: 83483
negative_passages.text: Is there a nice way to classify the ideals of the ring of lower triangular matrices?
negative_passages.docid: 95146
negative_passages.text: Polynomial ring $R[X] $ has zero Jacobson radical, for $R$ a domain
negative_passages.docid: 135046
negative_passages.text: Can this quick way of showing that $K[X,Y]/(Y-X^2)\cong K[X]$ be turned into a valid argument?
negative_passages.docid: 92517
negative_passages.text: Easy way to show that $\mathbb{Z}[\sqrt[3]{2}]$ is the ring of integers of $\mathbb{Q}[\sqrt[3]{2}]$