The Cocycle Equation on Commutative Semigroups

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• 作者：Bruce Ebanks (1)
  
  1. Department of Mathematics and Statistics ; Mississippi State University ; P.O. Box MA ; Mississippi State ; MS ; 39762 ; USA
  
• 关键词：39B52 ; 39B72 primary ; 39 ; 02 ; 20M50 ; 20M14 ; 20M15 ; 06A12 ; 20M10 secondary ; Commutative semigroup ; cocycle equation ; semilattice of semigroups ; archimedean semigroup ; separative semigroup ; epigroup
• 刊名：Results in Mathematics
• 出版年：2015
• 出版时间：February 2015
• 年：2015
• 卷：67
• 期：1-2
• 页码：253-264
• 全文大小：200 KB
• 参考文献：1. Acz茅l J.: The general solution of two functional equations by reduction to functions additive in two variables and with the aid of Hamel bases. Glas. Mat.-Fiz. Astron. II 20, 65鈥?3 (1965)
  2. Clifford, A.H., Preston, G.B.: Algebraic Theory of Semigroups, vol. 1. American Mathematical Society, Providence (1961)
  3. Davison T.M.K., Ebanks B.: Cocycles on cancellative semigroups. Publ. Math. Debrecen 46, 137鈥?47 (1995)
  4. Davison T.M.K., Ebanks B.: The cocycle equation on periodic semigroups. Aequationes Math. 56, 216鈥?21 (1998) CrossRef
  5. Ebanks B.: Branching measures of information on strings. Can. Math. Bull. 22, 433鈥?48 (1979) CrossRef
  6. Ebanks B.: Kurepa鈥檚 functional equation on semigroups. Stochastica 6, 39鈥?5 (1982)
  7. Ebanks, B.: General solution of the 2-cocycle functional equation on solvable groups. Aequationes Math. 73, 260鈥?79 (2007); erratum, Aequationes Math. 76, 315鈥?16 (2008)
  8. Ebanks B., Stetk忙r H.: Continuous cocycles on locally compact groups. Aequationes Math. 78, 123鈥?45 (2009) CrossRef
  9. Ebanks B., Stetk忙r H.: Continuous cocycles on locally compact groups II. Aequationes Math. 80, 57鈥?3 (2010) CrossRef
  10. Erd枚s J.: A remark on the paper 鈥極n some functional equations鈥?by S. Kurepa. Glas. Mat.-Fiz. Astron. II 14, 3鈥? (1959)
  11. Grillet P.A.: Commutative Semigroups. Kluwer Academic Publishing, Dordrecht/Boston/London (2001) CrossRef
  12. Hossz煤 M.: On a functional equation by S. Kurepa. Glas. Mat.-Fiz. Astron. II 18, 59鈥?0 (1963)
  13. Jessen B., Karpf A., Thorup A.: Some functional equations in groups and rings. Math. Scand. 22, 257鈥?65 (1968)
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Mathematics
  
• 出版者：Birkh盲user Basel
• ISSN：1420-9012

文摘

Although the general solution of the cocycle functional equation on abelian groups is well-known, the theory concerning solutions of that equation on commutative semigroups is far from complete. Here we introduce a framework which allows us to make a significant advance in the development of this theory.