Albu, TomaKara, YelizTercan, Adnan2024-06-242024-06-242021-01-201607-3606https://doi.org/10.2989/16073606.2020.1861488https://www.tandfonline.com/doi/abs/10.2989/16073606.2020.1861488https://hdl.handle.net/11452/42270This paper is a natural continuation of our previous joint paper [Albu, Kara, Tercan, Fully invariant-extending modular lattices, and applications (I), J. Algebra 517 (2019), 207-222], where we introduced and investigated the notion of a fully invariant-extending lattice, the latticial counterpart of a fully invariant-extending module. In this paper we introduce and investigate the latticial counter-part of the concept of a strongly FI-extending module defined by Birkenmeier, Park, Rizvi (2002) as a module M having the property that every fully invariant submodule of M is essential in a fully invariant direct summand of M. Our main tool in doing so, is again the very useful concept of a linear morphism of lattices introduced in the literature by Albu and Iosif (2013).eninfo:eu-repo/semantics/closedAccessModular latticeUpper continuous latticeLinear morphism of latticesFully invariant elementFully invariant-extending latticeStrongly fully invariant-extending latticeScience & technologyPhysical sciencesMathematicsArticle00060889810000135736745310.2989/16073606.2020.18614881727-933X