Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2401.16941 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866913215435243520 |
|---|---|
| author | Han, Gang Chen, Yulin Pan, Zhennan |
| author_facet | Han, Gang Chen, Yulin Pan, Zhennan |
| contents | Let $ L((T^{-1}))$ be the space of (inverse) Laurent serieswith coefficients in some field $L$. It has a standard degree map and the induced topology. With its usual addition and a new product on this space which is continuous and preserves the standard degree map, it will be a complete topological division ring, and called a deformed Laurent series ring. Under mild restrictions, we give the necessary and sufficient conditions for a product on $ L((T^{-1}))$ to make it a deformed Laurent series ring. Then we apply the above theory to construct the completions of the Weyl division ring $D_1$, over some field of characteristic 0, with respect to a class of discrete valuations on it. Such completions are topological division rings with nice properties. For instance, their valuation rings are non-commutative Henselian rings; the centralizer of each element not in the center is commutative. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_16941 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Deformed Laurent series rings and completions of the Weyl division ring Han, Gang Chen, Yulin Pan, Zhennan Rings and Algebras Let $ L((T^{-1}))$ be the space of (inverse) Laurent serieswith coefficients in some field $L$. It has a standard degree map and the induced topology. With its usual addition and a new product on this space which is continuous and preserves the standard degree map, it will be a complete topological division ring, and called a deformed Laurent series ring. Under mild restrictions, we give the necessary and sufficient conditions for a product on $ L((T^{-1}))$ to make it a deformed Laurent series ring. Then we apply the above theory to construct the completions of the Weyl division ring $D_1$, over some field of characteristic 0, with respect to a class of discrete valuations on it. Such completions are topological division rings with nice properties. For instance, their valuation rings are non-commutative Henselian rings; the centralizer of each element not in the center is commutative. |
| title | Deformed Laurent series rings and completions of the Weyl division ring |
| topic | Rings and Algebras |
| url | https://arxiv.org/abs/2401.16941 |