Proving that elements in a finite ring are zero divisors or units AND deducing that every finite integral is a field
14343
Every nonzero element in a finite ring is either a unit or a zero divisor
116000
Prove that prime ideals of a finite ring are maximal
80961
Prove that a commutative ring $F$ is a field iff $F[x]$ is a Principal Ideal Domain
91622
Help with proof that $\mathbb Z[i]/\langle 1 - i \rangle$ is a field.
107821
The ring of integers of $\mathbf{Q}[i]$
138826
To show that either $R$ is a field or $R$ is a finite ring with prime number of elements and $ab = 0$ for all $a,b \in R$.
152013
elementary ring proof with composition of functions and addition of functions as operations
155642
Understanding divison by monic polynomial in $R[x]$ where $R$ is an arbitrary ring
87078
Prove the following set is an ideal of the ring $Z[x]$
19838
Prove that in general the set of the right zero divisors is different from the set of left zero divisors in a ring R
151011
Fields - Proof that every multiple of zero equals zero
75315
How to prove that homomorphism from field to ring is injective or zero?
127002
Prove that for a nonzero element $a$ of a field $F$ with $q$ elements $a^{-1} = a^{q-2}$
109199
Prove that every nonzero prime ideal is maximal in $\mathbb{Z}[\sqrt{d}]$
3129
A commutative ring is a field iff the only ideals are $(0)$ and $(1)$
46795
Explicit construction of a finite field with $p^n$ elements
117005
Rules in the ring with coefficients in finite field $\mathbb{F}_p$