New posts in polynomial-rings

Prove that $R[x]$ is an integral domain if and only if $R$ is an integral domain. [duplicate]

Showing $k[X] \cong k[X,Y,Z]\big/{(Y-X^2,Z-X^3)}$

Exhibit the ideals of $\mathbb{Z}[x]/(2,x^3+1)$

Homomorphisms and automorphisms on polynomial rings

Gauss's Lemma Proof

Domain containing polynomial ring over field, if finitely generated generated as module over it, is free as module over it

Issues with ideals

Is $\Bbb Z_4 [X]$ an integral domain?

Divisibility of a general polynomial of a rational expression [closed]

Defining irreducible polynomials over polynomial rings

Irreducibility criteria for polynomials with several variables.

Let $R= \mathbb{Q}[x^2 ,x^3 ]$, the set of all polynomials over $\mathbb{Q}$ with no $x$ term. Show that the $\gcd$ of $x^5$ and $x^6$ does not exist

Determining if two ideals in $\mathbb{Q}[X,Y]$ are equal

Show $\mathbb Z[x]/(x^2-cx) \ncong \mathbb Z \times \mathbb Z$.

How to deal with polynomial quotient rings