Element invertible in integral extension of ring implies invertible in ring
127418
If ring $B$ is integral over $A$, then an element of $A$ which is a unit in $B$ is also a unit in $A$.
7034
Prove that $A+I$ is invertible if $A$ is nilpotent
109470
Proof of whether a specific element is in a commutative, invertible monoid.
107207
$A\subseteq B\subseteq C$ ring extensions, $A\subseteq C$ finite/finitely-generated $\Rightarrow$ $A\subseteq B$ finite/finitely-generated?
88307
Commutative property of ring addition
68753
Elements in finite field extensions
73689
A question about the equivalence relation on the localization of a ring.
97902
In a integral domain every prime element is irreducible
141410
Injective integral domains are fields
5893
On the commutative property of multiplication (domain of integers, possibly reals)
119052
Finding invertible elements in $\mathbb{Z}/m\mathbb{Z}$
75315
How to prove that homomorphism from field to ring is injective or zero?
84149
Prove that an infinite ring with finite quotient rings is an integral domain
37058
Induced maps in homology are injective
15137
Does $IJ=IK\implies J=K$ always hold for integral domain and finitely generated nonzero ideal $I$?
116955
Showing the existence of a certain kind of extension of a finitely generated algebra
42809
How can we show that $(I-A)$ is invertible?