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Let R be a ring and let ΩR be the set of maximal right ideals of R. An R-module M is called an sd-Rickart module if, for every nonzero endomorphism… Click to show full abstract
Let R be a ring and let ΩR be the set of maximal right ideals of R. An R-module M is called an sd-Rickart module if, for every nonzero endomorphism f of M, Imf is a fully invariant direct summand of M. We obtain a characterization for an arbitrary direct sum of sd-Rickart modules to be sd-Rickart. We also obtain a decomposition of an sd-Rickart R-module M provided that R is a commutative Noetherian ring and Ass(M) ∩ ΩR is a finite set. In addition, we introduce and study a generalization of sd-Rickart modules.
Keywords:
class dual;
rickart;
rickart modules;
dual rickart;
module
Journal Title: Ukrainian Mathematical Journal
Year Published: 2020
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Journal Title: Ukrainian Mathematical Journal
Year Published: 2020
Link to full text (if available)
Share on Social Media: Sign Up to like & get
recommendations!