Homomorphic couplings on the real quaternion field (Q1203516)

It is known that the only compact connected near-fields are the reals, the complex numbers and the Kalscheuer near-fields which are derived from the real quaternion field \(\mathbb{H}\) by certain homomorphic couplings. In this paper the author determines all homomorphic couplings on \(\mathbb{H}\) and characterizes those homomorphic couplings which yield topological near- fields. He gives necessary and sufficient conditions for two near-fields coupled to \(\mathbb{H}\) by homomorphic couplings to be isomorphic and concludes that the number of non-isomorphic near-fields of this type is \(2^{2^{\aleph_ 0}}\). Some specific examples of homomorphic couplings on \(\mathbb{H}\) are also presented.