Let $S$ be an integral extension ring of $R$. Then $S[x_1,\ldots, x_n]$ is an integral extension ring of $R[x_1,\ldots, x_n]$.
112099
Polynomial ring with integral coefficients is integral
121750
Let $R$ be a commutative, unital ring and let $I$ be an ideal of $R.$ Prove that if $I$ is maximal then $R/I$ is a field.
158311
What is the dimension of $R[[X]]$ where $R$ is a Noetherian ring?
109039
Does this "extension property" for polynomial rings satisfy a universal property?
118781
product of ideals in matrix ring
88307
Commutative property of ring addition
157585
Structure theorem of finite rings
148788
Polynomial ring ideal. Show that $(f) \cap R_N = (0) \iff f \notin R_N$
135699
Questions about a commutative ring with exactly three ideals
157605
$IS \mid JS$ implies that $I\mid J$ where $I$ and $J$ are ideals of a number ring contained in another number ring $S$
148208
In Noetherian ring $R$, ideal $I\subset R$, $P\in\mathrm{Ass}(I),P=I:a$ for some $a\in R$.
67706
If $R$ is a Noetherian ring then $R[[x]]$ is also Noetherian
40705
If $M$ is an $R$-module and $I\subseteq\mathrm{Ann}(M)$ an ideal, then $M$ has a structure of $R/I$-module
90314
Maximal ideals in $R[x]$
16602
Proving $M_n(I)\lhd M_n(R)$ and proofs about ideal rings.
69728
If $f$ divides $g$ in $S[x]$, show that $f$ divides $g$ in $R[x]$ for $R$ a sub-ring of $S$.
73689
A question about the equivalence relation on the localization of a ring.