query: Fact about Integrally closed domains.
positive_passages.docid: 22716
positive_passages.text: $A$ is integrally closed if and only if $A_P$ is integrally closed for all maximal ideals $P$ of $A$.
negative_passages.docid: 77735
negative_passages.text: When $\Bbb Z_n$ is a domain. Counterexample to $ab \equiv 0 \Rightarrow a\equiv 0$ or $b\equiv 0\pmod n$
negative_passages.docid: 7011
negative_passages.text: Integral domain with fraction field equal to $\mathbb{R}$
negative_passages.docid: 49126
negative_passages.text: For which $f,g \in k[t]$, $k[f,g]$ is integrally closed?
negative_passages.docid: 132289
negative_passages.text: Associates in Integral Domain
negative_passages.docid: 147722
negative_passages.text: Is there a nice example of integral domain $R$ and $s,t \in R$, with $Rs \cap Rt$ not principal but lcm($s,t$) exists?
negative_passages.docid: 123024
negative_passages.text: A Noetherian integral domain is a UFD iff $(f):(g)$ is principal
negative_passages.docid: 93118
negative_passages.text: How to show that if two integral domains are isomorphic, then their corresponding field of quotients are isomorphic?
negative_passages.docid: 73344
negative_passages.text: Definition of irreducible polynomial via the units of an integral domain.
negative_passages.docid: 99236
negative_passages.text: Interior of closure of an open set
negative_passages.docid: 85782
negative_passages.text: UFDs are integrally closed
negative_passages.docid: 85206
negative_passages.text: Verifying proof :an Ideal $P$ is prime Ideal if $R/P$ is an integral domain.
negative_passages.docid: 47474
negative_passages.text: Proving $|f(z)|$ is constant on the boundary of a domain implies $f$ is a constant function
negative_passages.docid: 23242
negative_passages.text: Commutative integral domain with d.c.c. is a field
negative_passages.docid: 132193
negative_passages.text: Why $\Bbb Z$ = (integers) is an integral domain?
negative_passages.docid: 149971
negative_passages.text: Closed unit disk homeomorphic to $\mathbb{R}^2$?
negative_passages.docid: 93621
negative_passages.text: Prove that $\mathbb{Z}[\omega]$ is an integral domain