MU02021 Algebraical Structures

Mathematical Institute in Opava
Summer 2014
Extent and Intensity
2/2/0. 6 credit(s). Type of Completion: zk (examination).
doc. RNDr. Hynek Baran, Ph.D. (lecturer)
doc. RNDr. Michal Málek, Ph.D. (seminar tutor)
Guaranteed by
doc. RNDr. Hynek Baran, Ph.D.
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 the course the students deepen the knowledge of linear algebra and get overview of constructions, typical properties and mutual differences between the most used algebraical structures.
  • 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.
    5. Lattices.
    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
Further comments (probably available only in Czech)
The course can also be completed outside the examination period.
Teacher's information
For the credit it is required to solve the credit exercises.
The exam is oral. For a successful graduation the exam it is necessary to prove at least basic knowledge of the taken subject.
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, Winter 2014, Winter 2015, Winter 2016, Winter 2017, Winter 2018, Winter 2019, Winter 2020, Winter 2021.
  • Enrolment Statistics (Summer 2014, recent)
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