The quotient of an ideal generated by idempotents of a prime ideal does not contain any idempotents
103518
If $J$ is the ideal generated by all idempotents in a prime ideal, then $R/J$ has only trivial idempotents
74558
Localization of ideals at all primes
21604
A complete ring with respect to an ideal
9806
$M$ finitely generated if submodule and quotient are finitely generated.
67342
Why does a minimal prime ideal consist of zerodivisors?
116453
Is any quotient of a Euclidean domain by a prime ideal a Euclidean domain?
85915
Principal prime ideals are minimal among prime ideals in a UFD
108767
Irreducible Components of the Prime Spectrum of a Quotient Ring and Primary Decomposition
67944
Nilpotent Elements and Intersection of Prime Ideals
16727
Intersection of finitely generated ideals
155745
Ideals of $\mathbb{Z}[X]$
106550
The bijection between homogeneous prime ideals of $S_f$ and prime ideals of $(S_f)_0$
40975
Quotient of the ring of integers of a number field by a prime ideal
92822
Finite number of elements generating the unit ideal of a commutative ring
86724
Example of a non-zero module that has no associated primes
117536
Why is the localization at a prime ideal a local ring?
111114
Prove that an ideal in $k[x,y]$ is a prime ideal