MU02021 Algebraical Structures

Mathematical Institute in Opava
Summer 2009
Extent and Intensity
2/2/0. 6 credit(s). Type of Completion: zk (examination).
Teacher(s)
prof. RNDr. Artur Sergyeyev, Ph.D., DSc. (lecturer)
Guaranteed by
prof. RNDr. Artur Sergyeyev, Ph.D., DSc.
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
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.
The course is also listed under the following terms Summer 1998, Summer 1999, Summer 2000, Summer 2001, Summer 2002, Summer 2003, Summer 2004, Summer 2005, Summer 2006, Summer 2007, Summer 2008, Summer 2010, Summer 2011, Summer 2012, Summer 2013, Summer 2014, Winter 2014, Winter 2015, Winter 2016, Winter 2017, Winter 2018, Winter 2019, Winter 2020, Winter 2021, Winter 2022, Winter 2023, Winter 2024.
  • Enrolment Statistics (Summer 2009, recent)
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