query: Annihilator of a finitely generated torsion module is nonzero?
positive_passages.docid: 152730
positive_passages.text: Example of a finitely generated faithful torsion module over a commutative ring
negative_passages.docid: 128043
negative_passages.text: $A^n=0$ for $A$ nilpotent without the use of minimal polynomial
negative_passages.docid: 77453
negative_passages.text: A zero-dimensional ring is Noetherian?
negative_passages.docid: 59687
negative_passages.text: Suppose $M$ is a finitely generated module over $R$ where $R$ is a Noetherian ring. Prove that $M$ is a noetherian module.
negative_passages.docid: 37677
negative_passages.text: Radical of $\mathfrak{gl}_n$
negative_passages.docid: 53335
negative_passages.text: Why isn't $\mathbb{C}[x,y,z]/(xz-y)$ a flat $\mathbb{C}[x,y]$-module
negative_passages.docid: 85987
negative_passages.text: Prove that $k[x,y,z,w]/(xy-zw)$, the coordinate ring of $V(xy-zw) \subset \mathbb{A}^4$, is not a unique factorization domain
negative_passages.docid: 122189
negative_passages.text: Show that $M[x]$ is a Noetherian $A[x]$-module.
negative_passages.docid: 139828
negative_passages.text: Finitely Presented Modules and Exact Sequences
negative_passages.docid: 86724
negative_passages.text: Example of a non-zero module that has no associated primes
negative_passages.docid: 92822
negative_passages.text: Finite number of elements generating the unit ideal of a commutative ring
negative_passages.docid: 137029
negative_passages.text: Prove that $\operatorname{Hom}_{\Bbb{Z}}(\Bbb{Q},\Bbb{Z}) = 0$ and show that $\Bbb{Q}$ is not a projective $\Bbb{Z}$-module.
negative_passages.docid: 128861
negative_passages.text: If $M$ isn't Noetherian, $M$ has a submodule maximal with respect to being not finitely generated.
negative_passages.docid: 102072
negative_passages.text: Simple $M_n(D)$-module with $D$ a division ring
negative_passages.docid: 38571
negative_passages.text: Localization of a total quotient ring of a reduced ring
negative_passages.docid: 83812
negative_passages.text: Artinian ring and faithful module of finite length
negative_passages.docid: 93111
negative_passages.text: Finiteness of the Algebraic Closure