No abstract

Let L be a compactly generated multiplicative lattice with 1 compact in which every finite product of compact elements is compact and u ∈ L be a radical element. Under this hypothesis, in this paper we extend the concepts such as Baer lattices, quasiregular lattices etc. to what we respectively call Baer lattices w.r.t. u, quasiregular lattices w.r.t. u etc. and using these concepts we extend here the results proved by D. D. Anderson, C. Jayaram and P. A. Phiri. In the course of the development, we add many fruitful concepts and results. Also we study nature and characterizations of different elements.