discipline

Pure Mathematics

subject

Lattice Theory

lecturers

Péter Pál Pálfy, Csaba Szabó

credits

2

period

 

curriculum

Partition lattices, every lattice can be embedded into a partition lattice. Free lattices, Whitman’s Condition, canonical form of the elements, the atoms of free lattices, free lattices are semidistributive, the operations are continuous. There exists a fixed point free monotone map. Closure systems. Complete algebraic and geometric lattices. Modular lattices. The free modular lattice generated by 3 elements. Jordan-Dedekind chain condition. Semimodular lattices. Distributive lattices. Lattices and geometry: subspace lattices of projective geometries. Arguesian Law, geomodular lattices. Coordinatization. Congruences of lattices. Lattice varieties. nsson’s Lemma. Complemented Lattices. The congruences of relatively complemented lattices. Subalgebra-lattices. Congruence lattices. The Grätzer-Schmidt theorem.

literature

 

form of tuition

Lecture

mode of assessment

written/oral exam