DOIAbstract
AbstractLetkbe a field of characteristic not two, letfh(x0,x1)∈k[x0,x1] be an irreducible homogeneous polynomial and denote the ring of elements of degree zero in the homogeneous localizationk[x0,x1]fhbyk[x0,x1](fh). For degfh=3 it is proved that the composition algebras overk[x0,x1](fh)not containing zero divisors are defined overkand that there is at most one (split) composition algebra not defined overk. For degfh=4 all composition algebras overk[x0,x1](fh)are enumerated and partly classified
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