On n-associative formal power series

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• 作者：Harald Fripertinger
• 关键词：n ; Associativity ; Formal power series
• 刊名：Aequationes Mathematicae
• 出版年：2016
• 出版时间：April 2016
• 年：2016
• 卷：90
• 期：2
• 页码：449-467
• 全文大小：570 KB
• 参考文献：1.Fripertinger H., Reich L., Schwaiger J., Tomaschek J.: Associative formal power series in two indeterminates. Semigroup Forum 88(3), 529–540 (2014)MathSciNet CrossRef MATH
  2.Fripertinger H., Schwaiger J.: On one-dimensional formal group laws in characteristic zero. Aequationes Mathematicae 89(3), 857–862 (2015)MathSciNet CrossRef MATH
  3.Halter-Koch F.: Associative power series. Aequationes Mathematicae 89(3), 765–769 (2015)MathSciNet CrossRef MATH
  4.Hazewinkel M.: Formal Groups and Applications. Academic Press, New York, San Francisco, London (1978)MATH
  5.Marichal, J.-L.: Aggregation Operators for Multicriteria Decision Aid. PhD thesis, University of Liége (1998)
  6.Marichal J.-L., Mathonet P.: A description of n-ary semigroups polynomial-derived from integral domains. Semigroup Forum 83(2), 241–249 (2011)MathSciNet CrossRef MATH
  7.Reich, L.: On iterative roots of the formal power series F(x) = x. In: Butković, D., et al. (eds.) Functional Analysis IV, Proceedings of the Postgraduate School and Conference held at Inter-University Center, Dubrovnik, Yugoslavia, Nov 10–17, 1993, vol. 43 of Various Publication Series, pp. 245–255. Aarhus Universitet (1994)
  
• 作者单位：Harald Fripertinger (1)
  
  1. Institut für Mathematik und Wissenschaftliches Rechnen, NAWI-Graz Universitä Graz, Heinrichstr. 36/4, 8010, Graz, Austria
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Analysis
  Combinatorics
  
• 出版者：Birkh盲user Basel
• ISSN：1420-8903

文摘

A formal power series \({F(x_{1}, \ldots, x_{n})\in\mathbb{C}[\![x_1,\ldots x_n]\!]}\) of order at least 1 is called n-associative, n ≥ 3, if $$F(F(x_{1}, \ldots, x_{n}), x_{n+1},\ldots,x_{2n-1})=\cdots= F(x_1,\ldots,x_{n-1},F(x_n,x_{n+1},\ldots,x_{2n-1})).$$ This notion generalizes associativity which is the special case of n = 2. We determine the set of all n-associative formal power series over \({\mathbb{C}}\), all convergent n-associative power series, and all commutative (or symmetric) n-associative formal power series. Moreover we study relations between n- and m-associativity for certain \({n,m\in\mathbb{N}}\) and determine the structure of associative families (F _n ) _{n ≥ 1} of formal power series \({F(x_{1}, \ldots, x_{n})\in\mathbb{C}[\![x_1,\ldots x_n]\!]}\). Mathematics Subject Classification 13F25 (Formal power series rings) 16Z05 (Computational aspects of associative rings) Keywords n-Associativity Formal power series Page %P Close Plain text Look Inside Reference tools Export citation EndNote (.ENW) JabRef (.BIB) Mendeley (.BIB) Papers (.RIS) Zotero (.RIS) BibTeX (.BIB) Add to Papers Other actions Register for Journal Updates About This Journal Reprints and Permissions Share Share this content on Facebook Share this content on Twitter Share this content on LinkedIn Related Content Supplementary Material (0) References (7) References1.Fripertinger H., Reich L., Schwaiger J., Tomaschek J.: Associative formal power series in two indeterminates. Semigroup Forum 88(3), 529–540 (2014)MathSciNetCrossRefMATH2.Fripertinger H., Schwaiger J.: On one-dimensional formal group laws in characteristic zero. Aequationes Mathematicae 89(3), 857–862 (2015)MathSciNetCrossRefMATH3.Halter-Koch F.: Associative power series. Aequationes Mathematicae 89(3), 765–769 (2015)MathSciNetCrossRefMATH4.Hazewinkel M.: Formal Groups and Applications. Academic Press, New York, San Francisco, London (1978)MATH5.Marichal, J.-L.: Aggregation Operators for Multicriteria Decision Aid. PhD thesis, University of Liége (1998)6.Marichal J.-L., Mathonet P.: A description of n-ary semigroups polynomial-derived from integral domains. Semigroup Forum 83(2), 241–249 (2011)MathSciNetCrossRefMATH7.Reich, L.: On iterative roots of the formal power series F(x) = x. In: Butković, D., et al. (eds.) Functional Analysis IV, Proceedings of the Postgraduate School and Conference held at Inter-University Center, Dubrovnik, Yugoslavia, Nov 10–17, 1993, vol. 43 of Various Publication Series, pp. 245–255. Aarhus Universitet (1994) About this Article Title On n-associative formal power series Journal Aequationes mathematicae Volume 90, Issue 2 , pp 449-467 Cover Date2016-04 DOI 10.1007/s00010-015-0372-0 Print ISSN 0001-9054 Online ISSN 1420-8903 Publisher Springer International Publishing Additional Links Register for Journal Updates Editorial Board About This Journal Manuscript Submission Topics Analysis Combinatorics Keywords 13F25 (Formal power series rings) 16Z05 (Computational aspects of associative rings) n-Associativity Formal power series Industry Sectors Finance, Business & Banking Authors Harald Fripertinger (1) Author Affiliations 1. Institut für Mathematik und Wissenschaftliches Rechnen, NAWI-Graz Universitä Graz, Heinrichstr. 36/4, 8010, Graz, Austria Continue reading... To view the rest of this content please follow the download PDF link above.