SubjectsSubjects(version: 850)
Course, academic year 2019/2020
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Binary Systems - NMAG440
Title in English: Binární systémy
Guaranteed by: Department of Algebra (32-KA)
Faculty: Faculty of Mathematics and Physics
Actual: from 2019
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: not taught
Language: English, Czech
Teaching methods: full-time
Guarantor: doc. RNDr. David Stanovský, Ph.D.
prof. RNDr. Aleš Drápal, CSc., DSc.
Class: M Mgr. MSTR
M Mgr. MSTR > Povinně volitelné
Classification: Mathematics > Algebra
Annotation -
Last update: doc. Mgr. et Mgr. Jan Žemlička, Ph.D. (12.09.2013)
Introduction to structural properties of some classes of binary algebras - quasigroups, loops, semigroups, medial and self-distributive groupoids.
Course completion requirements - Czech
Last update: prof. RNDr. Aleš Drápal, CSc., DSc. (26.02.2019)

Zkouška je ústní, s písemnou přípravou. Hodnocení zkoušky může být upraveno směrem k lepší známce, pokud student během semestru opakovaně úspěšně řešil průběžné zadaváné úlohy a úložky.

Literature -
Last update: doc. RNDr. David Stanovský, Ph.D. (12.09.2013)

J. M. Howie, An introduction to semigroup theory. Academic Press, 1976.

V. D. Belousov: Osnovy teorii kvazigrupp i lup. Nauka, Moskva, 1967

P. Dehornoy: Braids and Self-Distributivity, Birkhauser, Basel, 2000

H. Orlik Pflugfelder: Quasigroups and Loops: An Introduction, Heldermann Verlag, 1991

J. D. H. Smith: An Introduction to Quasigroups and Their Representations, Chapman & Hall/CRC, 2006

Syllabus -
Last update: doc. RNDr. David Stanovský, Ph.D. (12.09.2013)

1. Semigroups

Green theory

Regularity

Inverse semigroups (Vagner-Preston theorem, congruences)

2. Quasigroups and loops

Basic infrastructure and constructions, isotopy

Weakly associative loops

3. Medial and selfdistributive grupoids

Entry requirements -
Last update: doc. Mgr. et Mgr. Jan Žemlička, Ph.D. (17.05.2019)

Basics of general algebra.

 
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