abstract
- In [T. Albu, J. Castro Pérez and J. Ríos Montes, The lattice structure of all lattice preradicals on modular complete lattices, and applications (I), Bull. Math. Soc. Sci. Math. Roumanie 62(110) (2019) 3¿20.], we presented and investigated the latticial counterpart of the big lattice R-pr of all the preradicals on the category Mod-R of all unital right R-modules over an associative ring R with identity. In this paper, we continue the study of lattice preradicals, and we introduce the concepts of an idempotent lattice preradical and a lattice radical. For r a fixed lattice preradical we define an equivalence relation in ¿¿ pr and obtain interesting partitions of the lattice ¿¿ pr, where is the big lattice of all lattice preradicals on all modular complete lattices. © 2027 World Scientific Publishing Company.