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Example of an ideal which is not principal in the ring $\mathbb{Z} [x]$
August 15th, 2022
ideals
abstract-algebra
Let $M$ be a maximal ideal of a ring $R$. Is $M[x]$ a maximal ideal of $R[x]$?
August 1st, 2022
abstract-algebra
ideals
ring-theory
Prove that R is a field ↔ The only ideals in R are R(0) and (0).
January 23rd, 2020
ring-theory
ideals
abstract-algebra
The quotient ring $\mathbb{Z}[i]/(1 + i)$
June 5th, 2020
ring-theory
ideals
gaussian-integers
abstract-algebra
Find the maximal ideals of the ring $\mathbb{Z}_{36}$.
December 6th, 2020
abstract-algebra
ideals
Left ideals of matrix rings are direct sum of column spaces?
November 18th, 2020
matrices
ideals
ring-theory
abstract-algebra
Matrix rings and ideals
November 25th, 2020
ideals
discrete-mathematics
abstract-algebra
ring-theory
Nilpotent element in $\mathbb{Z}/12\mathbb{Z}$ - Ideal
August 1st, 2022
abstract-algebra
ideals
nilpotence
Consider the ideal $I=(x^2+1,y)$ in the polynomial ring $\mathbb{C}[x,y]$.Then which of the following is true
August 1st, 2022
ideals
ring-theory
Let $I$ and $J$ be ideals of a commutative ring $R$ such that $I + J = R$. Show that there is an ideal $K$ in $R$ with $R/K \cong R/I \times R/J$
August 1st, 2022
ideals
ring-homomorphism
ring-theory
If every prime ideal in a ring $R$ is finitely generated, then $R$ is Noetherian?
August 1st, 2022
commutative-algebra
noetherian
abstract-algebra
ideals
subring of rational numbers and its ideal
August 1st, 2022
ideals
ring-theory
vector-space-isomorphism
rational-numbers
field-theory
Let $R$ be a commutative ring with identity. Let $M$ be an ideal such that every element of $R-M$ is a unit. Then $R/M$ is a field.
May 31st, 2020
abstract-algebra
ring-theory
field-theory
ideals
A commutative ring with identity is a field if and only it has no nonzero proper ideals
August 1st, 2022
ideals
ring-theory
field-theory
Ideals of the ring of power set
December 12th, 2020
ring-theory
ideals
maximal-and-prime-ideals
abstract-algebra
Zero ideal is proper ideal
May 4th, 2020
ideals
abstract-algebra
Finding Radical of an Ideal
August 1st, 2022
ideals
algebraic-geometry
commutative-algebra
The contraction of prime ideal is prime
August 1st, 2022
abstract-algebra
ideals
Why does the ideal generated by x generate polynomials?
August 1st, 2022
ideals
Is $\langle x^2+1\rangle$ a maximal ideal in $Z[x]$? What about $\langle x^2+1,5\rangle$?
August 1st, 2022
maximal-and-prime-ideals
ideals
abstract-algebra
Polynomial of minimum degree definition?
March 21st, 2020
minimal-polynomials
abstract-algebra
ideals
principal-ideal-domains
Noetherian ring of Krull dimension $0$
April 28th, 2020
commutative-algebra
abstract-algebra
ring-theory
ideals
Prime avoidance lemma
August 1st, 2022
abstract-algebra
ideals
Non-zero prime ideals of $F[x]$ are maximal
February 15th, 2020
ideals
abstract-algebra
ring-theory
Polynomials with even constant term form an ideal in $\mathbb{Z}[x]$
November 27th, 2020
polynomials
ideals
abstract-algebra
How to prove this ideal is a prime ideal
August 1st, 2022
ideals
abstract-algebra
$R$ local ring, $I$ maximal ideal then $x\notin I$ implies $x$ unit
January 14th, 2020
abstract-algebra
ideals
ring-theory
maximal-and-prime-ideals
Is $\langle x^2 + 1\rangle$ a maximal ideal in $Q[x]$ or is it just a prime ideal?
August 1st, 2022
ideals
ring-theory
abstract-algebra
The set of all continuous functions with compact support is ideal??????
May 5th, 2020
ideals
How to prove that the intersection of ideals is an ideal
August 1st, 2022
abstract-algebra
ideals
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