Prime Ideals: $ab\:\in \:I$ such that $a\:\in \:I\:\:\vee \:\:b\in I$ vs. either $a\:\in \:I\:$ or $b\:\in \:I\:$ but not both?
36498
Is logical "or" exclusive or inclusive in prime ideal definition
17247
Localisation and prime ideals
116883
About ideals in a ring which is a $k$ vector space
50445
Explaining the product of two ideals
131497
Maximal ideal not containing the set of powers of an element is prime
85915
Principal prime ideals are minimal among prime ideals in a UFD
74558
Localization of ideals at all primes
83721
If a prime $p\mid ab$, then $p\mid a$ or $p\mid b\ $ [Euclid's Lemma]
108896
Prime ideal in a polynomial ring over an integrally closed domain
135682
Are distinct prime ideals in a ring always coprime? If not, then when are they?
97740
Homogeneous ideals are contained in homogeneous prime ideals
587
Ideal Generated by the Union of Two Ideals
111114
Prove that an ideal in $k[x,y]$ is a prime ideal
65536
Finitely generated ideals in a Boolean ring are principal, why?
252
Why doesn't $0$ being a prime ideal in $\mathbb Z$ imply that $0$ is a prime number?
37929
Classification of prime ideals of $\mathbb{Z}[X]$
106550
The bijection between homogeneous prime ideals of $S_f$ and prime ideals of $(S_f)_0$