query: Prove that every finite integral domain is a field.
positive_passages.docid: 151018
positive_passages.text: Proving that any finite integral domain is a field.
negative_passages.docid: 75899
negative_passages.text: Principal ideal domain with finitely many ideals
negative_passages.docid: 31049
negative_passages.text: If $p$ is an irreducible element of an integral domain $D$, and if $e$ belongs to $D^\ast$ prove that $ep$ is also ireducible
negative_passages.docid: 150239
negative_passages.text: In an integral domain every non-zero prime ideal is invertible implies every non-zero proper ideal is invertible.
negative_passages.docid: 29635
negative_passages.text: Fields finitely generated as $\mathbb Z$-algebras are finite?
negative_passages.docid: 149849
negative_passages.text: Let $F$ be a field and $f: \mathbb{Z} \to F$ be a ring epimorphism.
negative_passages.docid: 96132
negative_passages.text: $R$ integral domain : $u\in R^*, a \text{ is prime} \iff au \text{ is prime}$
negative_passages.docid: 13174
negative_passages.text: Show that $A[X]/(aX+b)$ is an integral domain
negative_passages.docid: 134458
negative_passages.text: Isomorphisms preserving integral domains and fields
negative_passages.docid: 6855
negative_passages.text: Subfields of finite fields
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: 551
negative_passages.text: Why is a finite integral domain always field?
negative_passages.docid: 33645
negative_passages.text: Proving that an integral domain has at most two elements that satisfy the equation $x^2 = 1$.
negative_passages.docid: 46047
negative_passages.text: Check whether the quotient ring $R:=\mathbb{C}[x,y,z]/(xy-z^2)$ is a field or an integral domain
negative_passages.docid: 11259
negative_passages.text: Prove $R\times S$ is not an integral domain
negative_passages.docid: 57669
negative_passages.text: A proof that $\mathbb{Z}_{p}$ is an integral domain if and only if $p$ is prime.
negative_passages.docid: 131943
negative_passages.text: How to directly prove that $M$ is maximal ideal of $A$ iff $A/M$ is a field?