Proving that an element of a ring annihilates a module
99677
Generalization of Cayley-Hamilton
50114
A question about direct sums and products of modules
151803
Prove that $R$ is commutative
59134
Proving idempotent elements in $\mathbb{Z}_n$
158426
Proving lemma about centrality of idempotent elements in a Ring with no nilpotent elements.
147157
Modules over commutative rings
111034
Why an R-module is an R/I-module precisely when it is annihilated by I?
19838
Prove that in general the set of the right zero divisors is different from the set of left zero divisors in a ring R
150986
For a Noetherian ring $R$, we have $\text{Ass}_R(S^{-1}M)=\text{Ass}_R(M)\cap \{P:P\cap S=\emptyset\}$
47630
Endomorphisms of modules satisfying chain conditions and counterexamples.
4790
Generators of a finitely generated free module over a commutative ring
87078
Prove the following set is an ideal of the ring $Z[x]$
7067
Torsion Modules Annihilators
8417
Natural $(R/I)$-module structure for an $R$-module $M$ annihilated by $I$
5802
Proving the universal mapping property for polynomial rings
98818
Quotient ring of a localization of a ring
30465
Determining which rings have a module which is not semisimple