example of commutative ring where two equal principal ideals have generators which do not differ by a unit
139934
In $\mathbb{Z}/(n)$, does $(a) = (b)$ imply that $a$ and $b$ are associates?
80088
What possible characteristics may a local commutative unital ring have?
133738
Can a ring without a unit element have a subring with a unit element?
86816
Example of two prime ideals whose intersection of the squares not equal to the square of the intersection
84663
$A$ local Noetherian ring with principal maximal ideal implies PIR?
96071
How to show that a prime ideal of height 2 can’t necessarily be generated by 2 elements? (Hartshorne exercise I.1.11)
18361
Does the unit generate the additive group in a unital ring with cyclic additive group?
133495
Example of a ring without Invariant Basis Property
104789
How to tell an ideal of integer polynomial ring is principal?
150986
For a Noetherian ring $R$, we have $\text{Ass}_R(S^{-1}M)=\text{Ass}_R(M)\cap \{P:P\cap S=\emptyset\}$
32741
Idempotents in a ring without unity (rng) and no zero divisors.
89864
Units in finite polynomial rings
60223
Two principal ideals coincide if and only if their generators are associated
9074
Example of non-isomorphic structures which are elementarily equivalent
120496
Examples of Non-Noetherian Valuation Rings
92822
Finite number of elements generating the unit ideal of a commutative ring
35222
Characterizing units in polynomial rings