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• W1480454399 abstract "It is well known that the Rickart property of rings is not a left-right symmetric property. We extend the notion of the left Rickart property of rings to a general module theoretic setting and define 𝔏-Rickart modules. We study this notion for a right R-module M R where R is any ring and obtain its basic properties. While it is known that the endomorphism ring of a Rickart module is a right Rickart ring, we show that the endomorphism ring of an 𝔏-Rickart module is not a left Rickart ring in general. If M R is a finitely generated 𝔏-Rickart module, we prove that End R (M) is a left Rickart ring. We prove that an 𝔏-Rickart module with no set of infinitely many nonzero orthogonal idempotents in its endomorphism ring is a Baer module. 𝔏-Rickart modules are shown to satisfy a certain kind of nonsingularity which we term “endo-nonsingularity.” Among other results, we prove that M is endo-nonsingular and End R (M) is a left extending ring iff M is a Baer module and End R (M) is left cononsingular." @default.
• W1480454399 created "2016-06-24" @default.
• W1480454399 creator A5033413517 @default.
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• W1480454399 date "2015-02-27" @default.
• W1480454399 modified "2023-09-26" @default.
• W1480454399 title "𝔏-Rickart Modules" @default.
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• W1480454399 doi "https://doi.org/10.1080/00927872.2014.888563" @default.
• W1480454399 hasPublicationYear "2015" @default.
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