Abstract
In this paper we introduce the notions of Rickart and Baer lattices and their duals. We show that part of the theory of Rickart and Baer modules can be understood just using techniques from the theory of lattices. For, we use linear morphisms introduced by T. Albu and M. Iosif. We focus on a submonoid with zero \(\mathfrak {m}\) of the monoid of all linear endomorphism of a lattice \(\mathcal {L}\) in order to give a more general approach and apply our results in the theory of modules. We also show that \(\mathfrak {m}\)-Rickart and \(\mathfrak {m}\)-Baer lattices can be characterized by the annihilators in \(\mathfrak {m}\) generated by idempotents as in the case of modules.
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Acknowledgements
The first author wants to thank “Programa de Becas Posdoctorales en la UNAM 2021” from the Universidad Nacional Autónoma de México (UNAM). The authors would like to thank the referee for his/her carefully reading and accurate comments which improved this manuscript.
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Medina-Bárcenas, M., Rincón Mejía, H. \(\mathfrak {m}\)-Baer and \(\mathfrak {m}\)-Rickart Lattices. Order (2023). https://doi.org/10.1007/s11083-023-09651-9
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DOI: https://doi.org/10.1007/s11083-023-09651-9