Showing that these two rings $\frac{R[T]}{(aT-1)}, R[a^{-1}]$ are isomorphism.
49121
Factorizing a polynomial $f$ in $A[x]$ (with $A$ commutative), where $f$ has a zero in its field of fractions
87946
Proving that the unities of a ring form a group under multiplication
42552
Localisation is isomorphic to a quotient of polynomial ring
22604
Can $R \times R$ be isomorphic to $R$ as rings?
83100
Prove that the center of a ring is a subring.
158232
Tensor product of a module with an ideal is isomorphic to their standard product
93017
Isomorphism between $\Bbb R$ and $\Bbb R(X)$?
45627
Find a sub-ring of M(2, $\mathbb{Q}$) which is isomorphic to $\mathbb{Q}$
17978
Isomorphism classes of $\mathbb{Z}[i]$ modules.
11573
Rings and some of their properties
149973
Showing the following coordinate rings are not isomorphic
52966
Rings, ideals and units-proof
44983
Isomorphism of R-modules
145722
Prove there is a bijection between the set of $R[x]$-module structures on $M$ and $\mathrm{End}_{R-\mathsf{Mod}}(M)$.
37928
Isomorphism between $D_{2n}/Z(D_{2n})$ and $D_n$
131082
Proof that $\mathbb R/[0,1]$ and $\mathbb R$ are homeomorphic
114640
Showing that an ideal is not a free $R-$module.