New posts in Polynomial Rings

To what ring is $\mathbb{Z}[X,Y,Z]/(X-Y, X^3-Z)$ isomorphic?

How can a ring of polynomials with coefficients in a field $k$, and in infinitely many variables be a subring of $k[x,y]$?

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

Subrings $A$ of $\mathbb{F}_p[x]$ such that $\dim_{\mathbb{F}_p}\mathbb{F}_p[x]/A=1$.

Zero divisors of $\mathbb{Z}_{7}[x] / (x^4+x^3-3)$ and inverse element of $\overline{x+1}$

Prime ideals in $\mathbb{Z}[X], \mathbb{Q}[X], \mathbb{F}_{19}[X]$.

$\Bbb R[X,Y]/(F) \cong \Bbb R[Z]$ and $F_X G_Y - G_X F_Y \in \Bbb R^*$

Show that the ideal generated by two polynomials is actually equivalent to the ideal generated by a single polynomial

A Field of Polynomials of a Linear Operator

How to deal with polynomial quotient rings