Abstract
ABSTRACT Let be a commutative ring and an -module. Then is a multiplication module if for each submodule of . The ideal of has proved useful in studying multiplication modules. We show that if is a faithful multiplication module, then an ideal of , the trace ideal of . Moreover, is an idempotent multiplication ideal of and . We also show that for a multiplication module , is an ideal of the endomorphism ring of and that where the inverse limit is taken over the finitely generated submodules of .
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