query: Finitely generated field is a finite field
positive_passages.docid: 16643
positive_passages.text: A slick proof that a field which is finitely generated as a ring is finite
negative_passages.docid: 136422
negative_passages.text: Two finite fields with the same number of elements are isomorphic
negative_passages.docid: 137858
negative_passages.text: Showing that $\mathbb{Z}[i]/I$ is a finite field whenever $I$ is a prime ideal, and also finding its cardinality?
negative_passages.docid: 83586
negative_passages.text: Finite fields and primitive elements
negative_passages.docid: 38028
negative_passages.text: finitely generated k-algebra and polynomial ring
negative_passages.docid: 74777
negative_passages.text: Solvability and reducibility of a polynomial in a "chain" of finite fields
negative_passages.docid: 20218
negative_passages.text: Is this field extension finite?
negative_passages.docid: 157074
negative_passages.text: The elements in the composite field $FK$
negative_passages.docid: 10885
negative_passages.text: Existence of irreducible polynomials over finite field
negative_passages.docid: 140938
negative_passages.text: Finitely generated projective module
negative_passages.docid: 127044
negative_passages.text: Prove that a finitely-generated free module has a finite basis
negative_passages.docid: 71608
negative_passages.text: A property of finite field of order $2^n$
negative_passages.docid: 125568
negative_passages.text: Construction of $p^n$ field
negative_passages.docid: 73652
negative_passages.text: Exhibiting an isomorphism between two finite fields
negative_passages.docid: 92677
negative_passages.text: Infinite algebraic extension of a finite field
negative_passages.docid: 140106
negative_passages.text: How to prove a finite field is not ordered?
negative_passages.docid: 93474
negative_passages.text: A Finite Boolean Ring is Generated by Finitely Many Copies of $\mathbb{Z} / 2 \mathbb{Z}$