Subjects

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Lattice Theory II - NALG129

Title:	Teorie svazů II
Guaranteed by:	Department of Algebra (32-KA)
Faculty:	Faculty of Mathematics and Physics
Actual:	from 2018
Semester:	summer
E-Credits:	3
Hours per week, examination:	summer s.:2/0, Ex [HT]
Capacity:	unlimited
Min. number of students:	unlimited
4EU+:	no
Virtual mobility / capacity:	no
State of the course:	cancelled
Language:	Czech
Teaching methods:	full-time
Teaching methods:	full-time

Annotation -

Last update: T_KA (05.05.2008)

Free lattice, lattice varieties, tensor product of lattices, representation of algebraic lattices.

Literature -

Last update: T_KA (05.05.2008)

G. Grätzer, General Lattice Theory, Birkhäuser Verlag, Basel-Boston Berlin, 1998.

P. Jipsen a H. Rose, Varieties of Lattices, Lecture Notes in Mathematics, Vol.1533, Springer-Verlag, Berlin-New York, 1992.

R. Freese, J. Ježek, J. B. Nation, Free Lattices, Mathematical Surveys and Monographs, Vol.42, American Mathematical Society, Providence, RI, 1995

Syllabus -

Last update: T_KA (05.05.2008)

Free lattices:

free lattice and free product, Whitman's conditions, free lattice generated by three elements, semidistributive lattices, covers in free lattices

Lattice varieties:

varieties and fully invariant congruence relations, structure of lattice varieties, equational bases

Tensor product:

tensor product of join-semilattices, capped product, tensor product and congruences

Representation of algebraic lattices:

Lampe's theorem, Kuratowski lemma, Dilworth's congruence lattice problem