A rank-nullity theorem between $\mathbb Z^n$ and $\mathbb Z^k$
69398
Rank-nullity theorem for free $\mathbb Z$-modules
3682
If $V = \text{null}(\textsf{T}-\lambda\textsf{I}) \oplus \text{range}(\textsf{T}-\lambda\textsf{I})$, then prove that $\textsf{T}$ is diagonalizable
102391
Abel summability under the hypothesis $a_n \ge 0$
18036
Localization by a non-nilpotent as a polynomial quotient
35034
Multiplicative inverses for $Z_n$
77735
When $\Bbb Z_n$ is a domain. Counterexample to $ab \equiv 0 \Rightarrow a\equiv 0$ or $b\equiv 0\pmod n$
35897
Proof of: $AB=0 \Rightarrow Rank(A)+Rank(B) \leq n$
59804
Show that the plane $\{su+tv|s,t \in\Bbb R\}$ in $\Bbb R^3$ is equal to the null space of some element of $(\Bbb R^3)^{*}$.
15387
Order of $GL(n, \mathbb Z_p)$
88598
Property of $\{0^n, 1^n, \ldots\}$
127591
How to prove that the collection of rank-k matrices forms a closed subset of the space of matrices?
79056
Prove that $\mathbb Z^n$ is not isomorphic to $\mathbb Z^m$ for $m\neq n$
59134
Proving idempotent elements in $\mathbb{Z}_n$
41026
How to prove and interpret $\operatorname{rank}(AB) \leq \operatorname{min}(\operatorname{rank}(A), \operatorname{rank}(B))$?
118452
how to prove $\mathbb Z_n$ has divisors of zero if and only if $n$ is not prime
128043
$A^n=0$ for $A$ nilpotent without the use of minimal polynomial
146664
The union of two linearly independent subsets