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Binary Systems - NMAG440

Title:	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 [HT]
Capacity:	unlimited
Min. number of students:	unlimited
4EU+:	no
Virtual mobility / capacity:	no
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

Opinion survey results Examination dates Schedule Noticeboard

Annotation -

Introduction to structural properties of some classes of binary algebras - quasigroups, loops, semigroups, medial and self-distributive groupoids.

Last update: Žemlička Jan, doc. Mgr. et Mgr., Ph.D. (12.09.2013)

Course completion requirements - Czech

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.

Last update: Drápal Aleš, prof. RNDr., CSc., DSc. (26.02.2019)

Literature -

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

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

Syllabus -

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

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

Entry requirements -

Basics of general algebra.

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