PROPERLY SEMIPRIME SELF-PP-MODULES

In an earlier paper [8] the authors introduced strongly and properly s emiprime modules. Here properly semiprime modules M are investigated u nder the condition that every cyclic submodule is M-projective (self-p p-modules). We study the idempotent closure of M using the techniques of Pierce stalks related to the central idempotents of the self-inject ive hull of M. As an application of our theory we obtain several resul ts on (not necessarily associative) biregular, properly semiprime, red uced and PI-rings. An example is given of an associative semiprime PSP ring with polynomial identity which coincides with its central closur e and is not biregular (see 3.6). Another example shows that a semipri me left and right FP-injective PI-ring need not be regular (see 4.8). Some of the results were already announced in [7].