Associative formal power series in two indeterminates

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• 作者：Harald Fripertinger (1)
  Ludwig Reich (1)
  Jens Schwaiger (1)
  J?rg Tomaschek (2)
  
• 关键词：Associativity ; Formal power series
• 刊名：Semigroup Forum
• 出版年：2014
• 出版时间：June 2014
• 年：2014
• 卷：88
• 期：3
• 页码：529-540
• 全文大小：
• 参考文献：1. Aczél, J.: Lectures on Functional Equations and Their Applications. Dover Publications, New York (2006)
  2. Cartan, H.: Elementary Theory of Analytic Functions of One or Several Complex Variables. Dover, New York (1995)
  3. Chéritat, A.: Fractions rationelles associatives et corps quadratiques. Rev. Des. Math. Enseign. Super. 109, 1025-040 (1998-999)
  4. G?azek, K., Gleichgewicht, B.: On 3-semigroups and 3-groups polynomial-derived from integral domains. Semigroup Forum 32(1), 61-0 (1985) rg/10.1007/BF02575523" target="_blank" title="It opens in new window">CrossRef
  5. Hazewinkel, M.: Formal Groups and Applications. Acad. Press, New York (1978)
  6. Marichal, J.-L., Mathonet, P.: A description of / n-ary semigroups polynomial-derived from integral domains. Semigroup Forum 83(2), 241-49 (2011) rg/10.1007/s00233-011-9295-9" target="_blank" title="It opens in new window">CrossRef
  
• 作者单位：Harald Fripertinger (1)
  Ludwig Reich (1)
  Jens Schwaiger (1)
  J?rg Tomaschek (2)
  
  1. Institut für Mathematik und Wissenschaftliches Rechnen, Karl-Franzens-Universit?t Graz, Heinrichstra?e 36, 8010, Graz, Austria
  2. Mathematics Research Unit, Université du Luxembourg, 6, rue Richard Coudenhove-Kalergi, 1359, Luxembourg, Grand Duchy of Luxembourg
  
• ISSN：1432-2137

文摘

Investigating the associativity equation for formal power series in two variables we show that the transcendental associative formal power series are of order one or two and that they can be represented by an invertible formal power series in one variable. We also discuss the convergence of associative formal power series.