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Course, academic year 2017/2018
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Lattice Theory 2 - NMAG466
Czech title: Teorie svazů 2
Guaranteed by: Department of Algebra (32-KA)
Faculty: Faculty of Mathematics and Physics
Actual: from 2016
Semester: summer
E-Credits: 3
Hours per week, examination: summer s.:2/0 Ex [hours/week]
Capacity: unlimited
Min. number of students: unlimited
State of the course: taught
Language: English
Teaching methods: full-time
Guarantor: Mgr. Pavel Růžička, Ph.D.
Class: M Mgr. MSTR
M Mgr. MSTR > Povinně volitelné
Classification: Mathematics > Algebra
Incompatibility : NALG129
Interchangeability : NALG129
Annotation -
Last update: T_KA (14.05.2013)

Free lattice, lattice varieties, tensor product of lattices, representation of algebraic lattices.
Literature -
Last update: T_KA (14.05.2013)

  • G. Grätzer, General Lattice Theory, Birkhäuser Verlag, Basel-Boston Berlin, 1998.
  • Garrett Birkhoff, Lattices theory, AMS, 1967.
  • 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 (14.05.2013)

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

 
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