New post in Ideals

Example of an ideal which is not principal in the ring $\mathbb{Z} [x]$

August 15th, 2022

Let $M$ be a maximal ideal of a ring $R$. Is $M[x]$ a maximal ideal of $R[x]$?

August 1st, 2022

Prove that R is a field ↔ The only ideals in R are R(0) and (0).

January 23rd, 2020

The quotient ring $\mathbb{Z}[i]/(1 + i)$

June 5th, 2020

Find the maximal ideals of the ring $\mathbb{Z}_{36}$.

December 6th, 2020

Left ideals of matrix rings are direct sum of column spaces?

November 18th, 2020

Matrix rings and ideals

November 25th, 2020

Nilpotent element in $\mathbb{Z}/12\mathbb{Z}$ - Ideal

August 1st, 2022

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

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

If every prime ideal in a ring $R$ is finitely generated, then $R$ is Noetherian?

August 1st, 2022

subring of rational numbers and its ideal

August 1st, 2022

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

A commutative ring with identity is a field if and only it has no nonzero proper ideals

August 1st, 2022

Ideals of the ring of power set

December 12th, 2020

Zero ideal is proper ideal

May 4th, 2020

Finding Radical of an Ideal

August 1st, 2022

The contraction of prime ideal is prime

August 1st, 2022

Why does the ideal generated by x generate polynomials?

August 1st, 2022

Is $\langle x^2+1\rangle$ a maximal ideal in $Z[x]$? What about $\langle x^2+1,5\rangle$?

August 1st, 2022

Polynomial of minimum degree definition?

March 21st, 2020

Noetherian ring of Krull dimension $0$

April 28th, 2020

Prime avoidance lemma

August 1st, 2022

Non-zero prime ideals of $F[x]$ are maximal

February 15th, 2020

Polynomials with even constant term form an ideal in $\mathbb{Z}[x]$

November 27th, 2020

How to prove this ideal is a prime ideal

August 1st, 2022

$R$ local ring, $I$ maximal ideal then $x\notin I$ implies $x$ unit

January 14th, 2020

Is $\langle x^2 + 1\rangle$ a maximal ideal in $Q[x]$ or is it just a prime ideal?

August 1st, 2022

The set of all continuous functions with compact support is ideal??????

May 5th, 2020

How to prove that the intersection of ideals is an ideal

August 1st, 2022