Let $(f_1,\ldots,f_r)\subset k[x_1,\ldots,x_n],(g_1,\ldots,g_s)\subset k[y_1,\ldots,y_m]$ be radical ideals. Then their sum is radical.
118513
Ideal of product of affine varieties
69649
If an ideal contains the multiplicative identity, then it is the whole ring
111114
Prove that an ideal in $k[x,y]$ is a prime ideal
37393
$R$ is commutative, $I$,$J$ are ideals, $I+J=R$, then $IJ=I\cap J$
96787
Why is the arbitrary sum, but not the arbitrary intersection, of ideals an ideal?
120181
The ideal generated by $2$ and $ x$ in $\mathbb{Z}[x]$
148788
Polynomial ring ideal. Show that $(f) \cap R_N = (0) \iff f \notin R_N$
114640
Showing that an ideal is not a free $R-$module.
80397
Show that this set of polynomials is ideal in F[x]
90314
Maximal ideals in $R[x]$
122012
The ideal $(x,y)$ is not a free $K[x,y]$-module
116943
Proof for maximal ideals in $\mathbb{Z}[x]$
27766
Comaximal ideals in a commutative ring
144250
subideals of an ideal
63736
Every radical ideal in a Noetherian ring is a finite intersection of primes
114343
If $I$ and $J$ are ideals in a ring $R$ with $1$ such that $I+J = R$, show that $I^m$ and $J^n$ are co-maximal for all $m,n \in \mathbb{N}$
129371
Maximal ideals in the ring of real functions on $[0,1]$