Radicals and Socles of Modules

Abstract:

      In §1, we discuss me properties or radicais of modures (derntion 1.1)to botain some decomposition properties of certain classes of modules. Szasz's theorem on semi-primitive MHL-rings (rings with DCC on principal left ideals. [7]) will then be deduced. The class of such rings lies between that of the semiprimitive Artinian rings and that of the semiprimitive rings; so Szasz's structure theorem presents a desirable intermediate to the classical Wedderburn-Artin theorem and the Jacobson the- orem([2], p. 14).