Prove that an element in the quotient field is actually in the ring itself
75009
$A = \bigcap_{\mathfrak{p} \in \text{Spec(A)}} A_{\mathfrak{p}} = \bigcap_{\mathfrak{m} \in \text{MaxSpec(A)}} A_{\mathfrak{m}}$
69649
If an ideal contains the multiplicative identity, then it is the whole ring
144789
identify the ring $\mathbb{Z}[x]/(2x-1)$
77862
Question about fields and quotients of polynomial rings
61292
How to know which elements are in the Quotient Ring $\mathbb{Z}[x]/\langle x, 2\rangle$?
142212
Let $q$ be a prime congruent to 3 mod 4, prove the quotient ring $\mathbb{Z}[i]/(q)$ is a field with $q^2$ elements
79535
Prove that $R$ is a commutative ring if $x^3=x$
114688
Show that a division ring is simple.
21604
A complete ring with respect to an ideal
40975
Quotient of the ring of integers of a number field by a prime ideal
124564
Prove the ring $a+b\sqrt[3]{2}+c\sqrt[3]{4}$ has inverse and is a field
80961
Prove that a commutative ring $F$ is a field iff $F[x]$ is a Principal Ideal Domain
81296
If A and B are ideals of a ring, show that A + B = $\{a+b|a \in A, b \in B\}$ is an ideal
75315
How to prove that homomorphism from field to ring is injective or zero?
99567
Proving that an inverse ring homomorphism of an ideal is an ideal?
91622
Help with proof that $\mathbb Z[i]/\langle 1 - i \rangle$ is a field.
157488
Proving that $k[x,y,z]/(xz - (y^2 + 1))$ is a normal ring.