query: $S$ is a subring of an integral domain $R$ which is finitely generated algebra over $S$, Jac(S)=0 implies Jac(R)=0
positive_passages.docid: 26138
positive_passages.text: Atiyah Macdonald Exercise 5.22
negative_passages.docid: 90599
negative_passages.text: Trouble with proving $A$ is an integrally closed domain $\Rightarrow$ $A[t]$ is integrally closed domain
negative_passages.docid: 79650
negative_passages.text: Division Rings and Division Algebras
negative_passages.docid: 138114
negative_passages.text: Proving the quotient of a principal ideal domain by a prime ideal is again a principal ideal domain
negative_passages.docid: 42652
negative_passages.text: Must $k$-subalgebra of $k[x]$ be finitely generated?
negative_passages.docid: 75899
negative_passages.text: Principal ideal domain with finitely many ideals
negative_passages.docid: 149412
negative_passages.text: Every prime ideal of a finitely generated $\mathbb{R}$-algebra is an intersection of maximal ideals?
negative_passages.docid: 27167
negative_passages.text: Ideals in $F[x]$ and Euclidean domains are generated by any element of minimal degree
negative_passages.docid: 76496
negative_passages.text: Showing that every field is an integral domain.
negative_passages.docid: 150206
negative_passages.text: Every finitely generated algebra over a field is a Jacobson 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: 2995
negative_passages.text: A finite dimensional algebra over a field has only finitely many prime ideals and all of them are maximal
negative_passages.docid: 141659
negative_passages.text: Every field is an integral domain
negative_passages.docid: 9806
negative_passages.text: $M$ finitely generated if submodule and quotient are finitely generated.
negative_passages.docid: 1020
negative_passages.text: Proving that $\mathbb{Z}[\sqrt{2}]$ is a Euclidean domain
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: 23242
negative_passages.text: Commutative integral domain with d.c.c. is a field