[Merged by Bors] - feat(LinearAlgebra/TensorProduct/Finiteness): add some finiteness results of tensor product #11859
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acmepjz
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acmepjz
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erdOne
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Apr 4, 2024
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LGTM. I'll wait if Riccardo wants to give it a look, and I'll maintainer-merge this tomorrow otherwise. |
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Sorry, I was a little busy. LGTM too, thanks! bors merge |
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mathlib-bors bot
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Apr 14, 2024
…ults of tensor product (#11859) - `TensorProduct.exists_multiset`, `TensorProduct.exists_finsupp_left`, `TensorProduct.exists_finsupp_right`, `TensorProduct.exists_finset`: any element of `M ⊗[R] N` can be written as a finite sum of pure tensors. See also `TensorProduct.span_tmul_eq_top`. - `TensorProduct.exists_finite_submodule_left_of_finite`, `TensorProduct.exists_finite_submodule_right_of_finite`, `TensorProduct.exists_finite_submodule_of_finite` and 3 more: any finite subset of `M ⊗[R] N` is contained in `M' ⊗[R] N'` for some finitely generated submodules `M'` and `N'` of `M` and `N`, respectively. Each of these 3 functions has 2 variants.
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Louddy
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Apr 15, 2024
…ults of tensor product (#11859) - `TensorProduct.exists_multiset`, `TensorProduct.exists_finsupp_left`, `TensorProduct.exists_finsupp_right`, `TensorProduct.exists_finset`: any element of `M ⊗[R] N` can be written as a finite sum of pure tensors. See also `TensorProduct.span_tmul_eq_top`. - `TensorProduct.exists_finite_submodule_left_of_finite`, `TensorProduct.exists_finite_submodule_right_of_finite`, `TensorProduct.exists_finite_submodule_of_finite` and 3 more: any finite subset of `M ⊗[R] N` is contained in `M' ⊗[R] N'` for some finitely generated submodules `M'` and `N'` of `M` and `N`, respectively. Each of these 3 functions has 2 variants.
atarnoam
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Apr 16, 2024
…ults of tensor product (#11859) - `TensorProduct.exists_multiset`, `TensorProduct.exists_finsupp_left`, `TensorProduct.exists_finsupp_right`, `TensorProduct.exists_finset`: any element of `M ⊗[R] N` can be written as a finite sum of pure tensors. See also `TensorProduct.span_tmul_eq_top`. - `TensorProduct.exists_finite_submodule_left_of_finite`, `TensorProduct.exists_finite_submodule_right_of_finite`, `TensorProduct.exists_finite_submodule_of_finite` and 3 more: any finite subset of `M ⊗[R] N` is contained in `M' ⊗[R] N'` for some finitely generated submodules `M'` and `N'` of `M` and `N`, respectively. Each of these 3 functions has 2 variants.
uniwuni
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Apr 19, 2024
…ults of tensor product (#11859) - `TensorProduct.exists_multiset`, `TensorProduct.exists_finsupp_left`, `TensorProduct.exists_finsupp_right`, `TensorProduct.exists_finset`: any element of `M ⊗[R] N` can be written as a finite sum of pure tensors. See also `TensorProduct.span_tmul_eq_top`. - `TensorProduct.exists_finite_submodule_left_of_finite`, `TensorProduct.exists_finite_submodule_right_of_finite`, `TensorProduct.exists_finite_submodule_of_finite` and 3 more: any finite subset of `M ⊗[R] N` is contained in `M' ⊗[R] N'` for some finitely generated submodules `M'` and `N'` of `M` and `N`, respectively. Each of these 3 functions has 2 variants.
callesonne
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Apr 22, 2024
…ults of tensor product (#11859) - `TensorProduct.exists_multiset`, `TensorProduct.exists_finsupp_left`, `TensorProduct.exists_finsupp_right`, `TensorProduct.exists_finset`: any element of `M ⊗[R] N` can be written as a finite sum of pure tensors. See also `TensorProduct.span_tmul_eq_top`. - `TensorProduct.exists_finite_submodule_left_of_finite`, `TensorProduct.exists_finite_submodule_right_of_finite`, `TensorProduct.exists_finite_submodule_of_finite` and 3 more: any finite subset of `M ⊗[R] N` is contained in `M' ⊗[R] N'` for some finitely generated submodules `M'` and `N'` of `M` and `N`, respectively. Each of these 3 functions has 2 variants.
Jun2M
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Apr 24, 2024
…ults of tensor product (#11859) - `TensorProduct.exists_multiset`, `TensorProduct.exists_finsupp_left`, `TensorProduct.exists_finsupp_right`, `TensorProduct.exists_finset`: any element of `M ⊗[R] N` can be written as a finite sum of pure tensors. See also `TensorProduct.span_tmul_eq_top`. - `TensorProduct.exists_finite_submodule_left_of_finite`, `TensorProduct.exists_finite_submodule_right_of_finite`, `TensorProduct.exists_finite_submodule_of_finite` and 3 more: any finite subset of `M ⊗[R] N` is contained in `M' ⊗[R] N'` for some finitely generated submodules `M'` and `N'` of `M` and `N`, respectively. Each of these 3 functions has 2 variants.
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TensorProduct.exists_multiset,TensorProduct.exists_finsupp_left,TensorProduct.exists_finsupp_right,TensorProduct.exists_finset:any element of
M ⊗[R] Ncan be written as a finite sum of pure tensors.See also
TensorProduct.span_tmul_eq_top.TensorProduct.exists_finite_submodule_left_of_finite,TensorProduct.exists_finite_submodule_right_of_finite,TensorProduct.exists_finite_submodule_of_finiteand 3 more:any finite subset of
M ⊗[R] Nis contained inM' ⊗[R] N'for some finitely generated submodules
M'andN'ofMandN, respectively.Each of these 3 functions has 2 variants.