query: Is $O_L$ a free $O_K$ module?
positive_passages.docid: 153589
positive_passages.text: Integral basis of an extension of number fields
negative_passages.docid: 140938
negative_passages.text: Finitely generated projective module
negative_passages.docid: 109080
negative_passages.text: Is the kernel of a map to a finitely presented module finitely generated?
negative_passages.docid: 136804
negative_passages.text: Computing $\mathrm{Hom}(\mathbb Z_n,\mathbb Z_m)$ as $\mathbb Z$-module
negative_passages.docid: 17304
negative_passages.text: Tensor product of two finitely-generated modules over a local ring is zero
negative_passages.docid: 25383
negative_passages.text: Morphism between quotient sheaf ($K_{X}/\mathcal{O}_{X}$) and $\bigoplus_{x\in\mathcal{X}}i_{x,*}(K(X)/\mathcal{O}_{X,x})$
negative_passages.docid: 123130
negative_passages.text: Showing an isomorphism between exterior products of a free module
negative_passages.docid: 103427
negative_passages.text: When is $\operatorname{Hom}_A(M,N)$ finitely generated?
negative_passages.docid: 70298
negative_passages.text: Are quotients of chain groups $C_n(X)/C_n(A)$ still free?
negative_passages.docid: 142699
negative_passages.text: Is $R/N(R)$ a faithfully flat $R$-module?
negative_passages.docid: 8417
negative_passages.text: Natural $(R/I)$-module structure for an $R$-module $M$ annihilated by $I$
negative_passages.docid: 70872
negative_passages.text: Isomorphism of quotient modules implies isomorphism of submodules?
negative_passages.docid: 25260
negative_passages.text: Extension of a morphism $k^*\rightarrow X$ to $\mathbb{P}^1\rightarrow \overline{X}$
negative_passages.docid: 145700
negative_passages.text: Module isomorphic to second dual
negative_passages.docid: 69384
negative_passages.text: Are the following modules free and/or isomorphic?
negative_passages.docid: 25609
negative_passages.text: Multiplicity of G-module
negative_passages.docid: 26368
negative_passages.text: Finitely generated graded modules over $K[x]$