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New posts in ideals
Verifying that the ideal $(x^3-y^2)$ is prime
abstract-algebra
commutative-algebra
ideals
Idempotents in a local ring
abstract-algebra
commutative-algebra
ring-theory
ideals
Prime ideal and nilpotent elements [closed]
abstract-algebra
ring-theory
ideals
Is the complement of a prime ideal closed under both addition and multiplication?
abstract-algebra
ring-theory
ideals
maximal-and-prime-ideals
Homogeneous ideals are contained in homogeneous prime ideals
commutative-algebra
ideals
graded-rings
If $I$ is a maximal ideal of $R$, why is $R/I$ a field?
commutative-algebra
ring-theory
ideals
What is a primary decomposition of the ideal $I = \langle xy, x - yz \rangle$?
ring-theory
commutative-algebra
ideals
Is an ideal which is maximal with respect to the property that it consists of zero divisors necessarily prime?
abstract-algebra
commutative-algebra
ring-theory
ideals
$(x_1-a_1, x_2-a_2)$ is a maximal ideal of $K[x_1,x_2]$ [duplicate]
abstract-algebra
ideals
Prime ideals in a finite direct product of rings
maximal-and-prime-ideals
abstract-algebra
ideals
Is a polynomial $f$ zero at $(a_1,\ldots,a_n)$ iff $f$ lies in the ideal $(X_1-a_1,\ldots,X_n-a_n)$?
abstract-algebra
polynomials
ideals
roots
Every element outside the maximal ideal of a local ring is a unit
abstract-algebra
ideals
maximal-and-prime-ideals
Left ideals of $M_n(K)$ [duplicate]
abstract-algebra
ring-theory
ideals
Class group and factorizations
number-theory
algebraic-number-theory
intuition
ideals
Extended ideals and algebraic sets
algebraic-geometry
commutative-algebra
ideals
Prove that $p^2$ is the principal ideal $(2)$.
abstract-algebra
ideals
integral-domain
If $I+J=R$, where $R$ is a commutative rng, prove that $IJ=I\cap J$.
abstract-algebra
ideals
rngs
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
Question on $(2, 1+\sqrt{-5})$ as a submodule of $\mathbb{Z}[\sqrt{-5}]$.
abstract-algebra
ring-theory
modules
ideals
free-modules
Tensor product of quotient rings [duplicate]
abstract-algebra
ring-theory
commutative-algebra
ideals
tensor-products
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