Toma Albu, Jaime Castro Pérez, José Ríos Montes: Some remarks on the category $\,\sigma [L]\,$ of all $L$-subgenerated lattices, 131-147

Abstract:

In this paper we present some remarks on the category $\,\sigma [L]\,$ of all subgenerated lattices by a modular complete lattice $L$, defined in [Albu, Dascalescu, Iosif, Lattices subgenerated by a lattice, and applications (I), in preparation] “somehow” related with the concept of product in $L$ of two lattices, introduced and studied in [Albu, Pérez, Ríos, Prime, irreducible, and completely irreducible lattice preradicals on modular complete lattices, J. Algebra Appl. (2022), DOI: 10.1142/S0219498822500979, to appear].

Key Words: Modular lattice, upper continuous lattice, linear morphism of lattice, fully invariant sublattice, fully invariant element, trace, generator.

2010 Mathematics Subject Classification: Primary 06C05; Secondary 06C99, 06B35, 16D80, 16N80, 16S90, 18E15.