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Radicals and complete distributivity in relatively normal lattices

Jiří Rachůnek (2003)

Mathematica Bohemica

Lattices in the class ℐℛ𝒩 of algebraic, distributive lattices whose compact elements form relatively normal lattices are investigated. We deal mainly with the lattices in ℐℛ𝒩 the greatest element of which is compact. The distributive radicals of algebraic lattices are introduced and for the lattices in ℐℛ𝒩 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...

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