If a commutative ring is not a domain then when are elements by definition associate?
16023
Are associates unit multiples in a commutative ring with $1$?
5594
Question about the Euclidean ring definition
46047
Check whether the quotient ring $R:=\mathbb{C}[x,y,z]/(xy-z^2)$ is a field or an integral domain
5893
On the commutative property of multiplication (domain of integers, possibly reals)
151794
Can an ideal in a commutative integral domain be its own square?
98540
If $F[x]$ is a principal domain does $F$ have to be necessarily a field?
134773
A domain is a field if it has a common multiple $\!\neq\! 0$ of all elements $\!\neq\! 0$
92420
Characteristic of  a Non-unital Integral Ring
143884
A non-noetherian ring with noetherian spectrum
5084
When is the completion of a ring a local ring ?
110726
Example of a non-gcd domain
84149
Prove that an infinite ring with finite quotient rings is an integral domain
119067
Basic Ring Theory Question involving the unit element
138670
If product of finite elements in a ring is a unit then can we say each element as unit
116916
What's the rationale for requiring that a field be a $\boldsymbol{non}$-$\boldsymbol{trivial}$ ring?
127418
If ring $B$ is integral over $A$, then an element of $A$ which is a unit in $B$ is also a unit in $A$.
67260
What happens if we change the definition of quotient ring to the one that does not have ideal restriction?