$M_{1} \oplus M_{2}$ is a cyclic $A$-module $\iff \rm{Ann}(M_1)+\rm{Ann}(M_2)=A$
32343
Converse to Chinese Remainder Theorem
135039
${\rm Aut}(G)$ is cyclic $\implies G$ is abelian
95379
Prove that $V = V_1 \oplus V_2$ in the following
80302
A module $M$ whose submodules and factor modules are semisimple but not semisimple itself
52461
Why does $(g^b \bmod m)^a \bmod m = (g^a \bmod m)^b \bmod m$?
5223
$\mathbb{Z}_m \times \mathbb Z_n$ is cyclic if and only if $\gcd(m,n)=1$
60777
Prove $\, a_1 \Bbb Z \cap \dotsb \cap a_r \mathbb{Z} = {\rm lcm}(a_1, \ldots, a_r) \Bbb Z$
44983
Isomorphism of R-modules
102938
$\Bbb F_2[X]$ modules with 8 elements
33025
What is the order of $(\mathbb{Z} \oplus \mathbb{Z})/ \langle (2,2) \rangle$ and is it cyclic?
127996
$M_1$ and $M_2$ are subgroups and $M_1/N=M_2/N$. Is $M_1\cong M_2$?
120035
Pattern in Isomorphisms between $\mathbb Z_m \times \mathbb Z_n$ and $\mathbb Z_{mn}$
4648
Proving that $\mathbb{Z}_m\oplus \mathbb{Z}_n \cong \mathbb{Z}_d\oplus \mathbb{Z}_l $ as groups, where $l=\mathrm{lcm}(m,n)$ and $d=\gcd(m,n)$
36987
A criterion of flat modules
145112
Show that the multiplicative group $(\mathbb{Z}/p\mathbb{Z})^*$ is cyclic
144122
A problem about an $R$-module that is both injective and projective.
73402
Showing that $(\mathbb{Z}/p^{a}\mathbb{Z})^*$ is a cyclic group