On complementing topological algebras

This paper is based on a part of my thesis written under the supervision of Professor A. Mallios (University of Athens). I wish to express my sincere thanks to him for constant help and stimulating advice during the preparation of this work.Translated from Itogi Nauki i Tekhniki, Seriya Sovremennaya Matematika i Ee Prilozheniya. Tematicheskie Obzory. Vol. 49, Functional Analysis-4, 1997.