If $\text{Ext}_R^1(A,I) = 0$ for all $A\in ob(_R\text{Mod})$, then $I\in ob(_R\text{Mod})$ is injective.
102879
$\operatorname{Ext}$ and injectives, respectively projectives
135511
$M_a =\{ f\in C[0,1] |\ f(a)=0 \}$ for $a$ $\in$ $[0,1]$. Is $M_a$ finitely generated in $C[0,1]$?
121395
Let $X$ and $Y$ be non-empty sets and let $f:X \rightarrow Y$. Prove that $ f^{ −1} :P(Y ) → P(X) $ is injective if, and only if, $f$ is surjective.
22869
Prove $[0, 1]$ and $(0, 1]$ are equinumerous by use of bijection
150986
For a Noetherian ring $R$, we have $\text{Ass}_R(S^{-1}M)=\text{Ass}_R(M)\cap \{P:P\cap S=\emptyset\}$
46863
Show that $g$ is injective
152438
Is the composition of two injective functions injective?
35953
Prove that a function is not injective
91962
In a ring $a*a=0$ then $a+a=0$
76674
Let $S:U\rightarrow V, \ T:V\rightarrow W$ and if $S$ and $T$ are both injective/surjective, is $T\circ S$ injective/surjective?
15695
Is ${\rm conv}({\rm ext}((C(X))_1))$ dense in $(C(X))_1$?
145722
Prove there is a bijection between the set of $R[x]$-module structures on $M$ and $\mathrm{End}_{R-\mathsf{Mod}}(M)$.
98696
Is the exponential map ever not injective?
36996
If $x^{2}-x\in Z(R)$ for all $x\in R$, then $R$ is commutative.
73235
Rings $R/I \cong h(R)/h(I)\,$ for injective ring hom $h$
23735
Divisible module which is not injective
153886
Existence of antiderivative on a part $I$ of $\mathbb{R}$