Showing that $A[x] \cap A[x^{-1}] $ is an integral extension of $A$ when $x$ is invertible and $x$ belongs to a bigger ring containing $A$
7903
Prove that $B[x] \cap B[x^{-1}]$ is integral over $B$
49578
Proving $a\mathbb{Z}\cap b\mathbb{Z}=[a,b]\mathbb{Z}$
77361
How to prove $|H|[K:K \cap (g^{-1}Hg)]=|K|[H:H \cap (gKg^{-1})]$?
155745
Ideals of $\mathbb{Z}[X]$
78950
Does this map extend to a unique automorphism of the polynomial ring of an integral domain?
5802
Proving the universal mapping property for polynomial rings
145722
Prove there is a bijection between the set of $R[x]$-module structures on $M$ and $\mathrm{End}_{R-\mathsf{Mod}}(M)$.
5526
Prove that $ℤ[i]^*= \{1,-1,i,-i\}$
145125
How to prove that $A^{-1} + B^{-1}$ is invertible given the conditions
133975
Localising a polynomial ring and non-maximal prime ideal
7034
Prove that $A+I$ is invertible if $A$ is nilpotent
87078
Prove the following set is an ideal of the ring $Z[x]$
116943
Proof for maximal ideals in $\mathbb{Z}[x]$
108896
Prime ideal in a polynomial ring over an integrally closed domain
157378
On an injective ring homomorphism from the ring of continuous functions to the ring of differentiable functions
99567
Proving that an inverse ring homomorphism of an ideal is an ideal?
42552
Localisation is isomorphic to a quotient of polynomial ring