Confusion about a simple proof of prime ideal implies irreducibility in UFD.
101637
Let $R$ be an integral domain. If $x \in R$ is prime, then $x$ is irreducible.
73095
Foundational proof for Mersenne primes
120149
Is the complement of a prime ideal closed under both addition and multiplication?
123024
A Noetherian integral domain is a UFD iff $(f):(g)$ is principal
137858
Showing that $\mathbb{Z}[i]/I$ is a finite field whenever $I$ is a prime ideal, and also finding its cardinality?
116000
Prove that prime ideals of a finite ring are maximal
107454
Why D/I is finite if I is a non-zero ideal of the ring of integers of a number field?
97902
In a integral domain every prime element is irreducible
135102
How do the definitions of "irreducible" and "prime" elements differ?
69710
Is it true that an ideal is primary iff its radical is prime?
78549
Any prime is irreducible
102422
Irreducibly of $x^5-x-1$ over $\mathbb{F}_3$
85206
Verifying proof :an Ideal $P$ is prime Ideal if $R/P$ is an integral domain.
104782
Polynomial irreducible - maximal ideal
141792
Slick proof the determinant is an irreducible polynomial
68202
Must an ideal generated by an irreducible element be a maximal ideal?
132665
Show $p(X)$ (over a field) is irreducible iff $p(X+a)$ is irreducible