Showing that $R[X]/(Xf-1) \cong R[1/f]$
42552
Localisation is isomorphic to a quotient of polynomial ring
98587
$\mathbb Z [X] / (X)$ isomorphic to $\mathbb Z[X] / (X+1)$ isomorphic to $\mathbb Z [X] / (X+2015)$
131082
Proof that $\mathbb R/[0,1]$ and $\mathbb R$ are homeomorphic
122581
Prove or disprove that $G_1/H_1 \cong G_2/H_2$
155165
Prove that $\mathbb F_8=\mathbb F_2[X]/(X^3+X+1)$
69160
Show that the functor that takes $R$ to the set of invertible elements of $R[X]/(X^2-a)$ is representable.
51898
Show that $\operatorname{Hom}_{R} (R,M) \cong M$
105363
$\mathbb Z^n/\langle (a,...,a) \rangle \cong \mathbb Z^{n-1} \oplus \mathbb Z/\langle a \rangle$
33586
Prove the field of fractions of $F[[x]]$ is the ring $F((x))$ of formal Laurent series.
80397
Show that this set of polynomials is ideal in F[x]
33196
show that A(T) is a group under operation of composition of functions
49806
Prove that $\frac{R/ \ker \phi}{(\ker \phi + J)/ \ker \phi} \cong \frac{S}{\phi(J)}$
19112
Ring $R= \mathbb Z_3[x]/\langle x^6-1\rangle$
60777
Prove $\, a_1 \Bbb Z \cap \dotsb \cap a_r \mathbb{Z} = {\rm lcm}(a_1, \ldots, a_r) \Bbb Z$
62566
Does $X\times S^1\cong Y\times S^1$ imply that $X\times\mathbb R\cong Y\times\mathbb R$?
152841
I want to show that $f(x)=x.f(1)$ where $f:R\to R$ is additive.
18330
Does $R[x] \cong S[x]$ imply $R \cong S$?