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1. • CommentRowNumber1.
   • CommentAuthorMike Shulman
   • CommentTimeJul 6th 2019
   • (edited Jul 8th 2019)
   • PermaLink
   Author: Mike Shulman
   Format: MarkdownItexCreated page about Novikov fields, another kind of generalized power series field. I'm looking for a good notation for these along the lines of $k[[x]]$ for power series rings, $k((x))$ for Laurent series fields, $k((x^G))$ for Hahn series fields; the only notation in the literature seems to be $\Lambda(k)$, which doesn't suggest its meaning to me and clashes with exterior algebras. <a href="https://ncatlab.org/nlab/revision/Novikov+field/1">v1</a>, <a href="https://ncatlab.org/nlab/show/Novikov+field">current</a>

   Created page about Novikov fields, another kind of generalized power series field. I’m looking for a good notation for these along the lines of $k[[x]]$ for power series rings, $k((x))$ for Laurent series fields, $k((x^G))$ for Hahn series fields; the only notation in the literature seems to be $\Lambda(k)$, which doesn’t suggest its meaning to me and clashes with exterior algebras.

   v1, current

2. • CommentRowNumber2.
   • CommentAuthorUlrik
   • CommentTimeJul 8th 2019
   • PermaLink
   Author: Ulrik
   Format: MarkdownItexHow about $k((x^{(G)}))$, using parentheses to indicate a finiteness condition, in analogy to $k^G$ and $k^{(G)}$? Or, simply $k_{\text{Nov}}((x^G))$ in analogy to $k_{\text{Puis}}((x^G))$ for the notation for (generalized) Puiseux series? (E.g. in Efrat's book.)

   How about $k((x^{(G)}))$, using parentheses to indicate a finiteness condition, in analogy to $k^G$ and $k^{(G)}$?

   Or, simply $k_{\text{Nov}}((x^G))$ in analogy to $k_{\text{Puis}}((x^G))$ for the notation for (generalized) Puiseux series? (E.g. in Efrat’s book.)

3. • CommentRowNumber3.
   • CommentAuthorMike Shulman
   • CommentTimeJul 8th 2019
   • PermaLink
   Author: Mike Shulman
   Format: MarkdownItexWhat does $k^{(G)}$ mean?

   What does $k^{(G)}$ mean?

4. • CommentRowNumber4.
   • CommentAuthorUlrik
   • CommentTimeJul 8th 2019
   • PermaLink
   Author: Ulrik
   Format: MarkdownItexFinitely supported functions. I think it's quite common; here's an [example reference](https://books.google.de/books?id=PUNwDwAAQBAJ&pg=PA649&lpg=PA649#v=onepage&q&f=false).

   Finitely supported functions. I think it’s quite common; here’s an example reference.

5. • CommentRowNumber5.
   • CommentAuthorMike Shulman
   • CommentTimeJul 8th 2019
   • PermaLink
   Author: Mike Shulman
   Format: MarkdownItexThat link doesn't work for me, but I'll take your word for it. However, finitely supported functions is *not* what we mean here!

   That link doesn’t work for me, but I’ll take your word for it. However, finitely supported functions is not what we mean here!

6. • CommentRowNumber6.
   • CommentAuthorUlrik
   • CommentTimeJul 8th 2019
   • PermaLink
   Author: Ulrik
   Format: MarkdownItexYes, I understood that, but I figured that the context was sufficiently different that the notational device could be reused to denote another finiteness condition. Besides, there is already the notation $k^{(G)}$ for the finitely supported functions, so then $k((x^{(G)}))$ must mean something different, but related to $k((x^G))$. Anyway, this perhaps illustrates that $k_{\text{Nov}}((x^G))$ is the safer choice.

   Yes, I understood that, but I figured that the context was sufficiently different that the notational device could be reused to denote another finiteness condition. Besides, there is already the notation $k^{(G)}$ for the finitely supported functions, so then $k((x^{(G)}))$ must mean something different, but related to $k((x^G))$.

   Anyway, this perhaps illustrates that $k_{\text{Nov}}((x^G))$ is the safer choice.

7. • CommentRowNumber7.
   • CommentAuthornLab edit announcer
   • CommentTimeJul 22nd 2019
   • PermaLink
   Author: nLab edit announcer
   Format: MarkdownItexFukaya Category Ammar Husain <a href="https://ncatlab.org/nlab/revision/diff/Novikov+field/3">diff</a>, <a href="https://ncatlab.org/nlab/revision/Novikov+field/3">v3</a>, <a href="https://ncatlab.org/nlab/show/Novikov+field">current</a>

   Fukaya Category

   Ammar Husain

   diff, v3, current