Binary Systems - NMAG440
Title: |
Binární systémy |
Guaranteed by: |
Department of Algebra (32-KA) |
Faculty: |
Faculty of Mathematics and Physics |
Actual: |
from 2016 to 2016 |
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: |
taught |
Language: |
English, Czech |
Teaching methods: |
full-time |
Teaching methods: |
full-time |
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Annotation -
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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.
Last update: doc. Mgr. et Mgr. Jan Žemlička, Ph.D. (12.09.2013)
Seznámení se strukturními vlastnostmi vybraných tříd binárních algeber - kvazigrupy, lupy, pologrupy, mediální a samodistributivní grupoidy. |
Literature -
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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
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
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Syllabus -
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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
Last update: doc. RNDr. David Stanovský, Ph.D. (12.09.2013)
1. Pologrupy
Greenova teorie
Regularita
Inverzní pologupy (Vagner-Prestonova věta, kongruence)
2. Kvazigrupy a lupy
Základní pojmy a konstrukce, izotopie
Slabě asociativní lupy
3. Mediální a samodistributivní grupoidy
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