Rings Satisfying the Inductive Condition for Homomorphic Chain of Left R-Modules

Abstract:

      In this paper, the following results are obtained Theorem 1 Let L(R) be the Levitzki radical of the ring R, then L(R) contains every nil one-sided ideal of R if and only if R satisfies the inductive condition for homomorphic chain of left R-modules on every Levitzki subset.Theorem 2 Let ring R= A + B, where A is a nil left ideal and B is a nil subrin of R, then R is locally nilpotent if and only if R satisfies the inductive condition for horaomorphic chain of left R-modules on every subset of R -L(R).