Abstract
LetR be a right noetherian ring. A moduleM R is called a Δ-module providedR satisfies the descending chain condition for annihilators of subsets ofM. For a Δ-module, a series 0⊂M 1⊂M 2⊂...⊂M n =M can be constructed in which the factorsM i /M i−1 are sums of, α i -semicritical modules where α1≦α2≦...≦α n . In this paper we utilize this series in studying Λ=End(M R ). It is shown that ifN={f∈Λ|Kerf is essential inM}, thenN is nilpotent. Specific bounds on the index of nilpotency are given in terms of this series. Further ifM is injective and α-smooth, the annihilators of the factors of this series are used to provide necessary and sufficient conditions for EndM R to be semisimple.
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