Associative Rational Functions in Two Variables

Joel V. Brawley (), Shuhong Gao () and Donald Mills ()
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Joel V. Brawley: Clemson University, Department of Mathematical Sciences
Shuhong Gao: Clemson University, Department of Mathematical Sciences
Donald Mills: Southeastern Louisiana University, Department of Mathematics

A chapter in Finite Fields and Applications, 2001, pp 43-56 from Springer

Abstract: Abstract A rational function R(x, y) over a field is said to be associative if $$ R(R(x,y),z) = R(x,R(y,z)). $$ Associative rational functions over a field define group laws on subsets of the field (plus the point at infinity). In this paper, all the associative rational functions of two variables over an arbitrary field are determined and consequently all the groups obtainable from such functions are determined as well.

Date: 2001
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DOI: 10.1007/978-3-642-56755-1_5

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