Show that this field is finite and count its elements
129438
Gaussian Integers and Quotient Rings
6827
To identify field $Z[i]/(3)$
127002
Prove that for a nonzero element $a$ of a field $F$ with $q$ elements $a^{-1} = a^{q-2}$
46565
Show that $\mathbb{Q}(\sqrt{2})$ is a field.
86174
Finding an isomorphism between these two finite fields
20218
Is this field extension finite?
121077
Product of all elements in finite group
46795
Explicit construction of a finite field with $p^n$ elements
137858
Showing that $\mathbb{Z}[i]/I$ is a finite field whenever $I$ is a prime ideal, and also finding its cardinality?
42677
Proving $(\alpha + \beta)^{p^n} = \alpha^{p^n} + \beta^{p^n}$ in a finite field
73652
Exhibiting an isomorphism between two finite fields
81354
The product of all the elements of a finite abelian group
13983
Show that If $R[X]$ is Euclidean domain then $R$ is a field
27021
Show that $Q[\sqrt3]$ is a field
16643
A slick proof that a field which is finitely generated as a ring is finite
97357
How many elements in a number field of a given norm?
140106
How to prove a finite field is not ordered?