query: Question about integrality and algebraic extension
positive_passages.docid: 16589
positive_passages.text: Field of fractions of integral extension is an algebraic extension
negative_passages.docid: 76496
negative_passages.text: Showing that every field is an integral domain.
negative_passages.docid: 139288
negative_passages.text: Formal proof that $e^x$ is not algebraic
negative_passages.docid: 45098
negative_passages.text: How do we prove the "lying over" property for integral extensions?
negative_passages.docid: 98968
negative_passages.text: $X$ is algebraic over $E$
negative_passages.docid: 123903
negative_passages.text: If $E/F$ is algebraic and every $f\in F[X]$ has a root in $E$, why is $E$ algebraically closed?
negative_passages.docid: 145594
negative_passages.text: Splitting of prime ideals in algebraic extensions
negative_passages.docid: 28272
negative_passages.text: Does such localization of integral extension preserve inclusion?
negative_passages.docid: 93681
negative_passages.text: Integral closure of $\mathbb{Z}$ in $\mathbb{C}$ is not finitely generated as a $\mathbb{Z}$-module?
negative_passages.docid: 20218
negative_passages.text: Is this field extension finite?
negative_passages.docid: 25793
negative_passages.text: Extension fields isomorphic to fields of matrices
negative_passages.docid: 19511
negative_passages.text: Is the sub-field of algebraic elements of a field extension of $K$ containing roots of polynomials over $K$ algebraically closed?
negative_passages.docid: 158525
negative_passages.text: Given a field, the field of algebraic elements over it in an algebraically closed field extension is again algebraically closed?
negative_passages.docid: 88690
negative_passages.text: $\int_a^b f(x)\mathrm dx=0$ for all $-\infty<a<b<\infty$ a,b rational implies $f=0$ a.e
negative_passages.docid: 111775
negative_passages.text: $\int_{-\infty}^{+\infty} e^{-x^2} dx$ with complex analysis
negative_passages.docid: 116955
negative_passages.text: Showing the existence of a certain kind of extension of a finitely generated algebra
negative_passages.docid: 52902
negative_passages.text: How to prove $\int_{\mathbb R^d}{(1+|x|^{2})^{-m}dx}$ is integrable?