MU:MU02021 Algebraical Structures - Course Information

MU02021 Algebraical Structures

Extent and Intensity

2/2/0. 6 credit(s). Type of Completion: zk (examination).

Teacher(s)

RNDr. Jiří Kupka, Ph.D. (lecturer)
doc. RNDr. Zdeněk Kočan, Ph.D. (seminar tutor)

Guaranteed by

doc. RNDr. Kristína Smítalová, CSc.
Mathematical Institute in Opava

Course Enrolment Limitations

The course is also offered to the students of the fields other than those the course is directly associated with.

fields of study / plans the course is directly associated with

• Applied Mathematics in Risk Management (programme MU, B1101)
• Applied Mathematics in Risk Management (programme MU, B1102)
• Geometry (programme MU, M1101)
• Mathematical Analysis (programme MU, M1101)
• Mathematical Methods in Economics (programme MU, B1101)
• Mathematics (programme MU, B1101)
• Physics for Secondary School Teachers (programme FPF, M1701 Fyz)
• Secondary School Teacher Traning in Physics and Mathematics (programme FPF, M1701 Fyz) (2)
• Secondary School Teacher Training in Mathematics (programme FPF, M7504)
• Secondary school teacher training in general subjects with specialization in Mathematics (programme FPF, M7504)

Course objectives (in Czech)

V rámci této přednášky si posluchač prohloubí znalosti lineární algebry a získá přehled o konstrukcích, typických vlastnostech a také vzájemných odlišnostech nejpoužívanějších algebraických struktur.

Syllabus (in Czech)

• 1) Algebraické struktury a podstruktury, generátory, homomorfismy, isomorfismy, kongruence, faktorové algebry, součiny.
  2) Pologrupy, monoidy, grupy, Lagrangeova věta, normální podgrupy, akce grup, orbita a stabilizátor, Burnsideova věta.
  3) Okruhy, pole, ideály.
  4) Moduly a vektorové prostory, sumy, volné moduly, tenzorový součin.
  5) Svazy.

Literature

recommended literature
• L. Bican, J. Rosický. Teorie svazů a univerzální algebra. Praha, 1989. info
• W. J. Gilbert. Modern Algebra with Applications. Wiley, New York, 1976. info
• S. MacLane, G. Birkhoff. Algebra. Bratislava, 1974. info

Language of instruction

Czech

Further comments (probably available only in Czech)

The course can also be completed outside the examination period.

• Enrolment Statistics (Summer 2008, recent)
  
• Permalink: https://is.slu.cz/course/sumu/summer2008/MU02021