Svaz Filtrů pseudo BL - algebry

Lucie Vašíčková

Master's thesis

The filter lattice of a pseudo BL-algebra

Abstract:

Tato práce se zabývá pseudo BL-algebrami a jejich základními vlastnostmi, popisuje vztah mezi pseudo MV- a pseudo BL-algebrami. Hlavním tématem jsou filtry a vlastnosti svazu filtrů pseudo BL-algeber. Dále je zde popsána korespondence mezi kongruencemi a normálními filtry. Na závěr se zabývá filtry a ideály pseudo MV-algeber a dokazuje, že svaz filtrů je izomorfní se svazem l-podgrup

Abstract:

This thesis is concerned with the pseudo BL-algebras and their basic properties. It describes the relationship between the pseudo MV- and pseudo BL-algebras. The main topics are filters and properties of the filter lattice of the pseudo BL-algebras. It describes the correspondence between congruences and normal filters. The conclusion of the thesis is dedicated to the filters and ideals of the pseudo MV-algebras and it proves, that filter lattice is isomorphic to the lattice of convex l-subgroups

Keywords

Pseudo BL-algebra, pseudo MV-algebra, filtr a normální filtr pseudo BL-algebry, reprezentovatelná pseudo BL-algebra, filtr a ideál pseudo MV-algebry, svaz filtrů, l-podgrupa

Keywords

Pseudo BL-algebra, pseudo MV-algebra, fiter and normal filter of the pseudo BL-algebra, representable pseudo Bl-algebra, filter and ideal of the pseudo MV-algebra, lattice of filters, l-subgroup

Language used: Czech

Date on which the thesis was submitted / produced: 16. 4. 2010

Thesis defence

• Date of defence: 6. 5. 2010
• Supervisor: Jan Kühr
• Reader: Michal Botur

Univerzita Palackého

Přírodovědecká fakulta

Master programme / field:
Matematika / Diskrétní matematika