On semi-injective lattices

Year 2025, Early Access, 1 - 29

Francisco Gonzalez-bayona Sebastian Pardo-guerra Manuel Gerardo Zorrilla-noriega , Hugo Alberto Rincon Mejia

https://doi.org/10.24330/ieja.1778490

Abstract

In a previous paper, we explored, in the context of the category $ \mathcal{L_M} $ of complete modular lattices and linear morphisms introduced by T. Albu and M. Iosif, the lattice-theoretic counterparts of semi-projective retractable modules and their ring of endomorphisms. In this work, we investigate the dual situation. That is, we introduce the concept of semi-injective coretractable lattices, and we study their relation to their monoid of endomorphisms.

Keywords

Complete modular lattice , semi-injective lattice , retractable lattice , Hopfian lattice , co-Hopfian lattice , monoid of lattice endomorphisms

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