The criterion of differentiability of functions of quaternion variable is used as the basis of some algebraic field theory. Its necessary consequences are free Maxwell and Yang-Mills equations. The differentiability equations may be integrated in twistor variables and are reduced to algebraic ones. In the article we present bisingular solution and its topological modifications. Related EM-fields appear to be just the well-known Born solution and its modifications with singular structure of ring-like and toroidal topology. General problems of the algebrodynamical approach are discussed.
Categories: gr-qc hep-th quant-ph