Show that cardinality of $\mathbb{Z}^n/T(\mathbb{Z}^n)$ equals the absolute value of the determinant of the matrix representing the homomorphism T
4998
Question on determinants of matrices changing between integer matrices
78298
On the nilpotence of the matrix $AB-BA$
13761
Automorphisms in $\mathbb{Z}_n$
20097
Cardinality of the quotient ring $\mathbb{Z}[x]/(x^2-3,2x+4)$
26661
Ring homomorphisms from $\mathbb{Z}_n$ to $\mathbb{Z}_m$
97009
Image of ring homomorphism $\phi : \mathbb{Z}[t] \to \mathbb{Q}$?
120010
Show that $\aleph_{\alpha}^{\aleph_{1}} = \aleph_{\alpha}^{\aleph_{0}}\cdot 2^{\aleph_1}$
102972
Cardinality of $\mathbb{R}^\mathbb{R}$ by diagonal argument
7938
Number of Homomorphisms from $\Bbb{Z}_m$ to $\Bbb{Z}_n$
92639
Prove that the family of open sets in $\mathbb{R}$ has cardinality equal to $2^{\aleph_0}$
65162
Show that $\dim H^0(\mathbb{P}^n, \mathcal{O}_{\mathbb{P}^n}(m)) = {n + m \choose n}$ if $m \geq 0$, and $0$ otherwise.
40321
$\operatorname{Aut}(\mathbb Z_n)$ is isomorphic to $U_n$.
129162
Show there is a surjective homomorphism from $\mathbb{Z}\ast\mathbb{Z}$ onto $C_2\ast C_3$
5699
The number of ring homomorphisms from $\mathbb{Z}_m$ to $\mathbb{Z}_n$
6171
Isomorphism between $\Bbb{Z}[\sqrt{d}]$ and a quotient of $\Bbb{Z}[X].$
98507
$\text{Aut}(F)$ is isomorphic to the multiplicative group of all $n\times n$ matrices over $\mathbb Z$
73402
Showing that $(\mathbb{Z}/p^{a}\mathbb{Z})^*$ is a cyclic group