On The Value Group Of The Transseries
Pacific Journal of Mathematics, ISSN: 1945-5844, Vol: 312, Issue: 2, Page: 335-354
2021
- 4Captures
Metric Options: Counts1 Year3 YearSelecting the 1-year or 3-year option will change the metrics count to percentiles, illustrating how an article or review compares to other articles or reviews within the selected time period in the same journal. Selecting the 1-year option compares the metrics against other articles/reviews that were also published in the same calendar year. Selecting the 3-year option compares the metrics against other articles/reviews that were also published in the same calendar year plus the two years prior.
Example: if you select the 1-year option for an article published in 2019 and a metric category shows 90%, that means that the article or review is performing better than 90% of the other articles/reviews published in that journal in 2019. If you select the 3-year option for the same article published in 2019 and the metric category shows 90%, that means that the article or review is performing better than 90% of the other articles/reviews published in that journal in 2019, 2018 and 2017.
Citation Benchmarking is provided by Scopus and SciVal and is different from the metrics context provided by PlumX Metrics.
Example: if you select the 1-year option for an article published in 2019 and a metric category shows 90%, that means that the article or review is performing better than 90% of the other articles/reviews published in that journal in 2019. If you select the 3-year option for the same article published in 2019 and the metric category shows 90%, that means that the article or review is performing better than 90% of the other articles/reviews published in that journal in 2019, 2018 and 2017.
Citation Benchmarking is provided by Scopus and SciVal and is different from the metrics context provided by PlumX Metrics.
Metrics Details
- Captures4
- Readers4
Article Description
Given a real closed field (K,C,., <), the possibility of defining an ordered exponential on it, that is, an ordered group isomorphism exp:(K,+,<)!.K>0; →(K,.<), is strictly connected to the properties of its natural valuation (i.e., the valuation whose valuation ring is given by the elements bounded in absolute value by some natural number). For example if an exponential exists, then the valuation group v.K/ is isomorphic to an additive complement of the valuation ring. In [Kuhlmann et al. 1997] it is shown that for ordered fields that are maximal with respect to their natural valuation this condition fails unless the value group is trivial (in which case K ⊆ R), so maximal nonarchimedean ordered fields do not admit an exponential. In [Kuhlmann and Shelah 2005] the same property is used, the other way around, to show that, given a regular uncountable cardinal κ, there is a nontrivial group M such that the field(Formula presented) of κ-bounded generalized series admits an exponential map.
Bibliographic Details
Mathematical Sciences Publishers
Provide Feedback
Have ideas for a new metric? Would you like to see something else here?Let us know