If $S$ is a quotient ring of $R$, then either $char(S)$ divides $char(R)$, or $char(S)=0$
113512
Characteristic of nonzero commutative rings with unity
82953
In a ring with no zero-divisors, for $(m,n) =1$, $a^m = b^m$ and $a^n = b^n$ $\iff a =b$
108767
Irreducible Components of the Prime Spectrum of a Quotient Ring and Primary Decomposition
66451
In a ring, how do we prove that a * 0 = 0?
100720
Negative quotients and their remainders
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 $a,b \in R$.
81743
Prime ideals in $C[0,1]$
19754
$\mathbb{R}$ \ $\mathbb{Q}$ and $\mathbb{R}^2\setminus\mathbb{Q}^2$ disconnected?
31263
Quotient rings of Gaussian integers
58135
Quotient group $SL(2,\mathbb{R})/SO(2,\mathbb{R})$
73689
A question about the equivalence relation on the localization of a ring.
69611
If $R$ and $S$ are rings then $R \times S$ is never a field
84751
How can it be possible to localize a ring at a set with zero divisors?
113248
Proving $r!$ divides the product of r succesive positive integers
150986
For a Noetherian ring $R$, we have $\text{Ass}_R(S^{-1}M)=\text{Ass}_R(M)\cap \{P:P\cap S=\emptyset\}$
150911
Prove that the ring is Artinian and find a composition series of ideals
46047
Check whether the quotient ring $R:=\mathbb{C}[x,y,z]/(xy-z^2)$ is a field or an integral domain