Prove that if $M$ is an $R-$ projective left module then $M/IM$ is an $R/I-$ projective left module.
52992
Proving that P/PJ is a projective right module over R/J
157236
Tensor product of modules.
154076
How to show this property of $\mathbb{RP}^{n}$.
85752
Show that $M=\frac{\mathbb{Z}^3}{\langle (3,3,1),(2,2,2)\rangle}$ is isomorphic to $\mathbb{Z} \oplus \mathbb{Z}_4$ as $\mathbb{Z}$-modules
134294
A (not necessarily unitary) $R$ module $M$ splits into $B\oplus C$ where $B$ is unitary and $RC=\{0\}$.
122958
$R/I$ is commutative iff $rs-sr \in I$
142699
Is $R/N(R)$ a faithfully flat $R$-module?
59687
Suppose $M$ is a finitely generated module over $R$ where $R$ is a Noetherian ring. Prove that $M$ is a noetherian module.
33063
Are all simple left modules over a simple left artinian ring isomorphic?
136804
Computing $\mathrm{Hom}(\mathbb Z_n,\mathbb Z_m)$ as $\mathbb Z$-module
142612
Matrix Ring of a Semisimple Ring
114916
$\mathbb Z_{mn}$ isomorphic to $\mathbb Z_m\times\mathbb Z_n$ whenever $m$ and $n$ are coprime
122189
Show that $M[x]$ is a Noetherian $A[x]$-module.
65873
A proof for Atiyah-Macdonald Exercise I.21.iii
142863
Show that every ideal of the matrix ring $M_n(R)$ is of the form $M_n(I)$ where $I$ is an ideal of $R$
27735
Morphism to Projective Space $\mathbb{P}^m$
14158
Prove that $R$ is an integral domain $\Leftrightarrow$ $R[x]$ is an integral domain