On semi-projective modular lattices

A. Haghany and M. Vedadi, as well as M. K. Patel, explored the relationship between a semi-projective and retractable module and its endomorphism ring. In this work, we study the lattice-theoretic counterparts of these results. To this end, we consider the category of linear modular lattices. Specifically, we show a relation between a retractable and semi-projective complete modular lattice and its monoid of endomorphisms.