Suppose R is a commutative ring, $A \in R_n$, and the homomorphism $f: R^n \to R^n$ defined by $f(b) = Ab$ is surjective. Show $f$ is an isomorphism.
45270
Surjective endomorphisms of finitely generated modules are isomorphisms
1686
Show that quotient rings are not isomorphic
2072
Demonstrate that if $f$ is surjective then $X = f(f^{-1}(X))$
70658
Isomorphism between quotient modules
61491
Complex Ring Isomorphism
18540
Isomorphism from $\mathbb{C}[G]$ to $\prod_{i=1}^h M_{n_i}(\mathbb{C})$.
64048
Describe all ring homomorphisms
137011
showing $\psi: R\to \mathbb C$ is ring isomorphism.
93017
Isomorphism between $\Bbb R$ and $\Bbb R(X)$?
153291
Why a ring homomorphism from a local ring will not map a non-unit to a unit？
89702
Let $R$ be a ring such that for all $a,b$ in $R$, $(a^2-a)b=b(a^2-a)$. Then $R$ is commutative
119648
For which $n$ and $k$ are there nontrivial homomorphisms from $S_n$ to $\mathbb{Z}/k\mathbb{Z}$?
129162
Show there is a surjective homomorphism from $\mathbb{Z}\ast\mathbb{Z}$ onto $C_2\ast C_3$
97009
Image of ring homomorphism $\phi : \mathbb{Z}[t] \to \mathbb{Q}$?
97999
Explain these ring isomorphisms
104757
If $f \circ g$ is surjective, then f is surjective
9562
Proving that surjective endomorphisms of Noetherian modules are isomorphisms and a semi-simple and noetherian module is artinian.