Supernilpotent radicals, special radicals and Baer radical in normal classes of product algebras. (Q1034330)

The radicals of rings and other algebraic structures have been extensively studied by \textit{K. I. Beidar, Y. Fong} and \textit{W.-F. Ke} [J. Algebra 201, No. 1, 328--356 (1998; Zbl 0911.16013)]. In 1993, \textit{E.\, R.\, Puczyłowski} [Algebra Univers. 39, No. 1, 53--60 (1993; Zbl 0784.08009)] established the theory of radicals in universal classes of objects, called ``algebras'', by using an axiomatic system, and characterized the general radical classes and the semisimple classes. In the present paper, the authors establish a general radical theory and give the supernilpotent radicals and the Baer radical in normal classes of product algebras. Moreover, they establish an axiomatic system for the normal classes of product algebras and give some examples of such classes.