If $ \operatorname{Ass}(M)= \operatorname{Assh}(M)$, then $M$ is a Cohen-Macaulay $R$-module?
40320
Suppose all the Associated Primes are Minimal.
117688
Prove that $\def\Aut{\operatorname{Aut}}\Aut(\mathbf{Z_{n}})\simeq \mathbf{Z_{n}^{*}}$
122853
Show that $\operatorname{rank}(A) = \operatorname{rank}(B)$
37570
$M + N$ and $M \cap N$ are finitely generated $A$-modules implies $M$ and $N$ finitely generated using exact sequences
12474
Does an injective endomorphism of a finitely-generated free R-module have nonzero determinant?
52461
Why does $(g^b \bmod m)^a \bmod m = (g^a \bmod m)^b \bmod m$?
83766
If $B$ is a graded $A$-algebra, then $\operatorname{Proj}B$ is an $A$-scheme
4652
Is $V$ a simple $\text{End}_kV$-module?
93031
How to show that $\mathbb{Z}$ with the operation $m*n=m+(-1)^m n$ is associative?
158232
Tensor product of a module with an ideal is isomorphic to their standard product
80302
A module $M$ whose submodules and factor modules are semisimple but not semisimple itself
145700
Module isomorphic to second dual
28324
Inverse image of the sheaf associated to a module
101095
Constructing an example s.t. $\operatorname{Hom}_R(M,N)$ is not finitely generated
43990
R is a commutative ring with $1\ne 0$ and $R^m \cong R^n$, then $m=n$
68449
$\operatorname{Supp}(M)=V(\operatorname{Ann}M)$ if $M$ is finitely generated
153508
Define a function $\alpha$ :Hom$_R$($R^n,M$) $\rightarrow M^n$ which is a $R$-module isomorphism.