New posts in maximal-and-prime-ideals

Spectrum of infinite product of rings

commutative-algebra schemes products maximal-and-prime-ideals affine-schemes

Pull back image of maximal ideal under surjective ring homomorphism is maximal

functions ring-theory ideals maximal-and-prime-ideals

Question about a proof involving local rings: $R$ has exactly $3$ ideals, show that if $a,b\in I$ then $ab=0$

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

Atiyah-Macdonald problem 3.8

commutative-algebra modules maximal-and-prime-ideals localization

Characterization of maximal multiplicatively closed subsets

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

Show that $R\cong R_P$, the ring of quotients of $R$ with respect to the multiplicative set $R-P$ if $R$ has exactly one prime ideal $P$.

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

Proof that ideals in $C[0,1]$ are of the form $M_c$ that should not involve Zorn's Lemma

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

Number of elements in the ring $\mathbb Z [i]/\langle 2+2i\rangle$

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

Show that a radical ideal has no embedded prime ideals. [closed]

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

Normality of localizations in polynomial rings?

abstract-algebra commutative-algebra maximal-and-prime-ideals regular-rings

Exercise with localization and minimal primes

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

One-to-one correspondence of ideals in the quotient also extends to prime ideals?

abstract-algebra ideals maximal-and-prime-ideals

Examples of prime ideals that are not maximal

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

Maximal ideals in the ring of real functions on $[0,1]$ [closed]

abstract-algebra analysis ideals maximal-and-prime-ideals

A (non-artificial) example of a ring without maximal ideals

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

Maximal ideal in the ring of continuous functions from $\mathbb{R} \to \mathbb{R}$

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

Show that any prime ideal from such a ring is maximal.

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

Nonconstant polynomials do not generate maximal ideals in $\mathbb Z[x]$

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

Do the rings $\mathbb{Z}[x]$ or $\mathbb{Q}[x]$ have a quotient isomorphic to the field with 9 elements?

abstract-algebra field-theory ideals finite-fields maximal-and-prime-ideals

Classification of prime ideals of $\mathbb{Z}[X]$

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