If $(a) = (b)$, does there exists a unit $u$ such that $a = ub$ for commutative ring?
10908
Associated elements in a ring
20613
Units (invertibles) of polynomial rings over a field
5893
On the commutative property of multiplication (domain of integers, possibly reals)
126672
Product of principal ideals: $(a)\cdot (b) = (a b)$
145600
Is it true that $ U \oplus W_1 = U \oplus W_2 \implies W_1 = W_2 $?
83798
Does $A$ a UFD imply that  $A[T]$ is also a UFD?
27899
Can we prove the existence of $A\cup B$ without the union axiom?
103830
Each element of a ring is either a unit or a nilpotent element iff the ring has a unique prime ideal
36996
If $x^{2}-x\in Z(R)$ for all $x\in R$, then $R$ is commutative.
22604
Can $R \times R$ be isomorphic to $R$ as rings?
76826
Are there sets $A$ and $B$ such that $A \in B$ and $B \in A$?
22563
Units and Nilpotents
99715
Proper ideal and units proof
129025
Quotient ring local if Ring is local
150309
Why do we assume $a+b=b+a$ in a Ring with 1. Also, is it true with Rings without 1?
50908
Showing a Ring and an Ideal are equal
80088
What possible characteristics may a local commutative unital ring have?