On semi-injective lattices

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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