THE COLOMBEAU QUATERNION ALGEBRA

We introduce and investigate the topological algebra of Colombeau Generalized quaternions, H. This is an important object to study if one wants to build the algebraic theory of Colombeau generalized numbers. We classify the dense ideals of K, in the algebraic sense and prove that it has a maximal ring of quotients which is Von Neumann regular. Using the classification of the dense ideals we give a criteria for a generalized holomorphic function to satisfy the identity theorem.