Prove that a ring of fractions is a local ring
117536
Why is the localization at a prime ideal a local ring?
63447
Prove that the kernel of a homomorphism is a principal ideal. (Artin, Exercise 9.13)
19112
Ring $R= \mathbb Z_3[x]/\langle x^6-1\rangle$
84663
$A$ local Noetherian ring with principal maximal ideal implies PIR?
45971
Complete local ring which is not complete valuation ring
52966
Rings, ideals and units-proof
133975
Localising a polynomial ring and non-maximal prime ideal
57732
Rings of fractions and homomorphisms
34323
Prove that $a^{(p-1)/2} \equiv 1$ (mod p) and $a^{(p-1)/2} \equiv -1 \pmod p$
133706
If R is a local ring, then its maximal left-ideal is a left and right ideal
31933
$x^2 = 1$ in the ring $\mathbb{Z}/n \mathbb{Z}$
154495
Prove that a nontrivial subring of a ring that is a domain has the same identity
84149
Prove that an infinite ring with finite quotient rings is an integral domain
9794
Quotient ring of Gaussian integers $\mathbb{Z}[i]/(a+bi)$ when $a$ and $b$ are NOT coprime
23721
Prove that the Gaussian Integer's ring is a Euclidean domain
96144
Every element outside the maximal ideal of a local ring is a unit
69649
If an ideal contains the multiplicative identity, then it is the whole ring