Let $A$ be a local ring, $M$ and $N$ finitely generated $A$-modules. Show that if $M \otimes N = 0$ then $M=0$ or $N=0$
17304
Tensor product of two finitely-generated modules over a local ring is zero
122189
Show that $M[x]$ is a Noetherian $A[x]$-module.
150986
For a Noetherian ring $R$, we have $\text{Ass}_R(S^{-1}M)=\text{Ass}_R(M)\cap \{P:P\cap S=\emptyset\}$
101473
Tensor product of a sheaf of module and a residue field
26661
Ring homomorphisms from $\mathbb{Z}_n$ to $\mathbb{Z}_m$
76047
Annihilators of elements of a finitely generated faithful module over a noetherian reduced ring
69373
Prove that $(0)$ is a radical ideal in $\mathbb{Z}/n\mathbb{Z}$ iff $n$ is square free
37960
Zero Divisors in Direct Product of Rings
98818
Quotient ring of a localization of a ring
141258
Why does $M \mathbin{\otimes_R} N \cong M_\mathfrak{p} \mathbin{\otimes_{R_\mathfrak{p}}} N$?
63568
Ring with finitely many zerodivisors
38571
Localization of a total quotient ring of a reduced ring
66451
In a ring, how do we prove that a * 0 = 0?
30752
Proof of $(\mathbb{Z}/m\mathbb{Z}) \otimes_\mathbb{Z} (\mathbb{Z} / n \mathbb{Z}) \cong \mathbb{Z}/ \gcd(m,n)\mathbb{Z}$
118781
product of ideals in matrix ring
16602
Proving $M_n(I)\lhd M_n(R)$ and proofs about ideal rings.
38028
finitely generated k-algebra and polynomial ring