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Rickart and Dual Rickart Objects in Abelian Categories: Transfer via Functors

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Abstract

We study the transfer of (dual) relative Rickart properties via functors between abelian categories, and we deduce the transfer of (dual) relative Baer property. We also give applications to Grothendieck categories, comodule categories and (graded) module categories, with emphasis on endomorphism rings.

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Authors and Affiliations

  1. Department of Mathematics, Babeş-Bolyai University, Str. M. Kogălniceanu 1, 400084, Cluj-Napoca, Romania

    Septimiu Crivei

  2. Department of Statistics-Forecasts-Mathematics, Babeş-Bolyai University, Str. T. Mihali 58-60, 400591, Cluj-Napoca, Romania

    Gabriela Olteanu

Authors
  1. Septimiu Crivei
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  2. Gabriela Olteanu
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Corresponding author

Correspondence to Septimiu Crivei.

Additional information

Communicated by M. M. Clementino.

We would like to thank the referee for comments and suggestions, which improved the presentation of the paper. We acknowledge the support of the Grant PN-II-ID-PCE-2012-4-0100.

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Crivei, S., Olteanu, G. Rickart and Dual Rickart Objects in Abelian Categories: Transfer via Functors. Appl Categor Struct 26, 681–698 (2018). https://doi.org/10.1007/s10485-017-9509-8

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  • DOI: https://doi.org/10.1007/s10485-017-9509-8

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