MU02021 Algebraical Structures

Mathematical Institute in Opava
Winter 2022
Extent and Intensity
2/2/0. 6 credit(s). Type of Completion: zk (examination).
Teacher(s)
doc. RNDr. Zdeněk Kočan, Ph.D. (lecturer)
RNDr. Petr Blaschke, Ph.D. (seminar tutor)
Guaranteed by
doc. RNDr. Michal Marvan, CSc.
Mathematical Institute in Opava
Prerequisites (in Czech)
TYP_STUDIA(B)
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
During the course the students deepen the knowledge of algebra and gain an overview of constructions, typical properties and mutual differences between the most frequent algebraical structures.
Syllabus
  • 1. Algebraical structures and substructures, generators, homomorphisms, isomorphisms, congruences, factor algebras, products.
    2. Semigroups, monoids, groups, Lagrange theorem, normal subgroups, group actions, orbit and stabilizer, Burnside's theorem.
    3. Rings, fields, ideals.
    4. Modules and vector spaces, sums, free modules, tensor product.
Literature
    required literature
  • M. Marvan. Algebraické struktury. 2014. URL info
  • L. Bican, J. Rosický. Teorie svazů a univerzální algebra. Praha, 1989. info
    recommended literature
  • 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)
Study Materials
The course can also be completed outside the examination period.
Teacher's information
A written credit test with the passing score set at 70 %.
The exam is oral and tests the knowledge and understanding of the subject, including the proofs.
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 2009, 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 2023, Winter 2024.
  • Enrolment Statistics (Winter 2022, recent)
  • Permalink: https://is.slu.cz/course/sumu/winter2022/MU02021