Introduction In the last few years a few monographs dedicated to the theory of topolog- ical rings have appeared Warn27], Warn26], Wies 19], Wies 20], ArnGM]. Ring theory can be viewed as a particular case of Z-algebras. Many general results true for rings can be extended to algebras over commutative rings. In topological algebra the structure theory for two classes of topological algebras is well developed: Banach algebras; and locally compact rings...