1. Radicals and complete distributivity in relatively normal lattices
- Creator:
- Rachůnek, Jiří
- Format:
- bez média and svazek
- Type:
- model:article and TEXT
- Subject:
- relatively normal lattice, algebraic lattice, complete distributivity, closed element, and radical
- Language:
- English
- Description:
- Lattices in the class TRN of algebraic, distributive lattices whose compact elements form relatively normal lattices are investigated. We deal mainly with the lattices in TRN the greatest element of which is compact. The distributive radicals of algebraic lattices are introduced and for the lattices in TRN with the sublattice of compact elements satisfying the conditional join-infinite distributive law they are compared with two other kinds of radicals. Connections between complete distributivity of algebraic lattices and the distributive radicals are described. The general results can be applied e.g. to MV -algebras, GMV -algebras and unital l-groups.
- Rights:
- http://creativecommons.org/publicdomain/mark/1.0/ and policy:public