$A$ has only finitely many minimal prime ideals $\implies\ (0)$ is decomposable?
108767
Irreducible Components of the Prime Spectrum of a Quotient Ring and Primary Decomposition
85915
Principal prime ideals are minimal among prime ideals in a UFD
149412
Every prime ideal of a finitely generated $\mathbb{R}$-algebra is an intersection of maximal ideals?
74558
Localization of ideals at all primes
19230
Prime/Maximal Ideals in $\mathbb{Z}[\sqrt d]$
78380
Dedekind domain with a finite number of prime ideals is principal
36631
Is $[0,1] \cap \Bbb Q$ a compact subset of $\Bbb Q$?
62917
Associated Prime Ideals in a Noetherian Ring; Exercise 6.4 in Matsumura
17247
Localisation and prime ideals
53469
C(0, 1) has infinitely many prime ideals not of the form Mp
45575
why each left ideal of this is minimal?
76813
The ring $ℤ/nℤ$ is a field if and only if $n$ is prime
107370
An open covering of $\mathbb{Q} \cap [0,1]$ that does not contain any finite subcovering
3327
Height and minimal number of generators of an ideal
13901
Finitely many prime ideals lying over $\mathfrak{p}$
146801
Primary decomposition of an ideal
27167
Ideals in $F[x]$ and Euclidean domains are generated by any element of minimal degree