New posts in maximal-and-prime-ideals

Question about a proof: $U$ maximal among non-finitely generated ideals of $R$, then $U$ is a prime ideal.

abstract-algebra ring-theory maximal-and-prime-ideals

Question from the proof of the thread dealing with showing an ideal maximal in the set of ideals not intersecting multiplicative sets is prime.

abstract-algebra ring-theory maximal-and-prime-ideals

What's so special about a prime ideal?

ring-theory ideals maximal-and-prime-ideals

(Unique) OR (unique + nontrivial) prime ideal

abstract-algebra ring-theory commutative-algebra ideals maximal-and-prime-ideals

How to turn elements of a ring $A$ into functions on $\text{Spec}A$?

ring-theory commutative-algebra definition ideals maximal-and-prime-ideals

Must a ring (commutative, with 1), in which every non-zero ideal is prime, be a field?

abstract-algebra ring-theory commutative-algebra examples-counterexamples maximal-and-prime-ideals

Spectrum of $\mathbb{Z}^\mathbb{N}$

abstract-algebra algebraic-geometry ring-theory commutative-algebra maximal-and-prime-ideals

Maximal Ideals of Different Heights

ring-theory commutative-algebra examples-counterexamples maximal-and-prime-ideals

Is the complement of a prime ideal closed under both addition and multiplication?

abstract-algebra ring-theory ideals maximal-and-prime-ideals

Zorn's Lemma and Prime Ideals

abstract-algebra ring-theory commutative-algebra maximal-and-prime-ideals

Prime ideals in a finite direct product of rings

maximal-and-prime-ideals abstract-algebra ideals

Every element outside the maximal ideal of a local ring is a unit

abstract-algebra ideals maximal-and-prime-ideals

Prove that prime ideals of a finite ring are maximal

abstract-algebra ring-theory maximal-and-prime-ideals finite-rings

A prime ideal of a polynomial ring over a PID can be generated by two elements. [duplicate]

abstract-algebra maximal-and-prime-ideals principal-ideal-domains

Shorter proof of $R/I$ is a field if and only if $I$ is maximal

abstract-algebra proof-verification ring-theory ideals maximal-and-prime-ideals

Every prime ideal in $\mathbb{Z}[x]$ is generated by at most two elements [duplicate]

abstract-algebra ring-theory ideals maximal-and-prime-ideals

Is logical "or" exclusive or inclusive in prime ideal definition

abstract-algebra ideals maximal-and-prime-ideals

Is there an example of a power of prime ideal in a polynomial ring that is not primary?

abstract-algebra polynomials ring-theory commutative-algebra maximal-and-prime-ideals

Ring of $\mathbb{Z}_2$-valued functions

ring-theory maximal-and-prime-ideals idempotents

Ideal in a ring of continuous functions

abstract-algebra ring-theory continuity ideals maximal-and-prime-ideals