query: Problem regarding proving a field to be finite.
positive_passages.docid: 21079
positive_passages.text: Why must a field whose a group of units is cyclic be finite?
negative_passages.docid: 154610
negative_passages.text: Number of solutions for the given equation in finite field of order 32.
negative_passages.docid: 151018
negative_passages.text: Proving that any finite integral domain is a field.
negative_passages.docid: 29626
negative_passages.text: Is there a proper subfield $K\subset \mathbb R$ such that $[\mathbb R:K]$ is finite?
negative_passages.docid: 10548
negative_passages.text: The equation $-1 = x^2 + y^2$ in finite fields
negative_passages.docid: 73454
negative_passages.text: Prove that $f$ has finite number of roots
negative_passages.docid: 120215
negative_passages.text: Sum of elements of a finite field
negative_passages.docid: 140808
negative_passages.text: Problem on Galois theory and irreducible polynomial
negative_passages.docid: 106737
negative_passages.text: A problem on field extension
negative_passages.docid: 127656
negative_passages.text: How to prove that if $A$ is infinite and $B$ is finite, then $|A\cup B|=|A|$?
negative_passages.docid: 61428
negative_passages.text: Show that an algebraically closed field must be infinite.
negative_passages.docid: 138826
negative_passages.text: To show that either $R$ is a field or $R$ is a finite ring with prime number of elements and $ab = 0$ for all $a,b \in R$.
negative_passages.docid: 122828
negative_passages.text: Proof that TREE(n) where n >= 3 is finite?
negative_passages.docid: 46795
negative_passages.text: Explicit construction of a finite field with $p^n$ elements
negative_passages.docid: 92677
negative_passages.text: Infinite algebraic extension of a finite field
negative_passages.docid: 12134
negative_passages.text: divisibility question in abstract algebra over a field
negative_passages.docid: 128437
negative_passages.text: How to prove that a finite set is countable