Nailin Guan
Nailin Guan
Proving that there is always an open normal subgroup in a clopen nhd of compact topological group Co-authored-by: NailinGuan Yi Song Xuchun Li --- - [x] depends on: #16980 -...
Prove that any profinite group is limit of finite groups. --- - [ ] depends on: #16976 - [x] depends on: #16980 - [ ] depends on: #16991 [![Open in...
In this PR, we proved every finitely generated module over regular local ring has finite projective dimension. With this and Auslander Buchsbaum theorem, we can obtain the global dimension of...
In this PR, we defined the concept of maximal Cohen Macaulay module, and proved that finitely generated maximal Cohen Macaulay module over regular local ring is free. --- - [...
In this PR, we defined the depth of two modules as the minimal order of nonvanishing `Ext` and the `I-depth` for ideal `I` and some basic properties. Including the equivalence...
In this PR we proved for a (comm)ring `R`, `R` is Cohen-Macaulay ring iff the unmixed theorem holds (for every ideal `I` of height `r` generated by `r` elements, all...
We prove Cohen Macaulay local ring is catenary. Following Theorem 31, Chater 6, _Commutative Algebra_, Matsumura --- - [ ] depends on: #26218 [](https://gitpod.io/from-referrer/)
polynomial over Cohen Macaulay ring is Cohen Macaulay --- [](https://gitpod.io/from-referrer/)
In this PR, we added the definition of CM module, CM local ring (extending local ring), and CM ring. We also proved Theorem 30, Chater 6, _Commutative Algebra_, Matsumura. ---...
This PR mainly proved the Ischbecke theorem, stating that `depth(N,M)` is greater or equal to `depth(M) - dim(N)` for finitely generated module `N, M` over local ring. --- - [...