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Lattice Theory - NALG109

Title:	Teorie svazů
Guaranteed by:	Department of Algebra (32-KA)
Faculty:	Faculty of Mathematics and Physics
Actual:	from 2018
Semester:	winter
E-Credits:	3
Hours per week, examination:	winter 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

Guarantor:	doc. Mgr. Pavel Růžička, Ph.D.
Classification:	Mathematics > Algebra
Interchangeability :	NMAG435
Is incompatible with:	NMAG435
Is interchangeable with:	NMAG435

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Annotation -

Last update: T_KA (05.05.2008)

Introduction to the lattice theory: structure and basic properties of distributive and modular lattices, structure of congruences of lattices, free lattices, lattice varieties.

Literature -

Last update: T_KA (05.05.2008)

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

Garrett Birkhoff, Lattices theory, AMS, 1967.

Syllabus -

Last update: T_KA (05.05.2008)

Basic properties of lattices:

lattices as ordered sets, algebraic concept, homomorphisms, congruences and ideals, join-irreducible elements

Distributive lattices:

characterization, free distributive lattices, congruences of distributive lattices, topological representation

Congruences and ideals:

weak projectivity and perspectivity, distributive, standard and neutral elements and ideals, congruences of a cartesian product, modular and weakly modular lattices, distributivity of the congruence lattice of a lattice

Modular and semimodular lattices:

characterization, Kurosh-Ore theorem, congruences in modular lattices, von Neumann theorem, Birghoff theorem, semimodular lattices, Jordan-Hölder theorem, geometric lattices, partition lattices, complemented modular lattices and projective geometries