M3150 Algebra II

Faculty of Science
Autumn 2009
Extent and Intensity
2/2/0. 4 credit(s) (fasci plus compl plus > 4). Type of Completion: zk (examination).
Teacher(s)
prof. RNDr. Radan Kučera, DSc. (lecturer)
Mgr. Jan Herman (seminar tutor)
Guaranteed by
prof. RNDr. Radan Kučera, DSc.
Department of Mathematics and Statistics - Departments - Faculty of Science
Timetable
Wed 8:00–9:50 M2,01021
  • Timetable of Seminar Groups:
M3150/01: Wed 16:00–17:50 M3,01023, J. Herman
Prerequisites (in Czech)
M2150 Algebra I
Zvládnutí základů matematiky a kurzu Algebra I.
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
At the end of this course, students should be able to:
* understand rudiments of group theory, ring theory and lattice theory;
* understand rudiments of universal algebra;
* explain basic notions and relations among them.
Syllabus
  • Rings and polynomials (ideals, factorrings, fields, skewfields, extensions, finite fields, symmetric polynomials).
  • Lattices (semilattices and lattices - two approaches, modular and distributive lattices, Boolean algebras, representation of finite distributive lattices and Boolean algebras).
  • Universal algebra (subalgebras, homomorphisms, congruences and factoralgebras, products, terms, varieties, free algebras, Birkhoff's theorem).
Literature
  • ROSICKÝ, Jiří. Algebra. 4., přeprac. vyd. Brno: Masarykova univerzita, 2002. 133 s. ISBN 80-210-2964-1. info
  • BICAN, Ladislav and Jiří ROSICKÝ. Teorie svazů a univerzální algebra. 1. vyd. Praha: Ministerstvo školství, mládeže a tělovýchovy ČSR, 1989. 84 s. info
  • PROCHÁZKA, Ladislav. Algebra. 1. vyd. Praha: Academia, 1990. 560 s. info
Teaching methods
Lectures: theoretical explanation. Exercises: solving problems with the aim to understand basic concepts and theorems, homeworks.
Assessment methods
Examination consists of two parts: written test and oral examination.
Language of instruction
Czech
Further comments (probably available only in Czech)
Study Materials
The course is taught annually.
Listed among pre-requisites of other courses
Teacher's information
http://www.math.muni.cz/~kucera
The course is also listed under the following terms Autumn 2007 - for the purpose of the accreditation, Autumn 1999, Autumn 2010 - only for the accreditation, Spring 2003, Autumn 2003, Autumn 2004, Autumn 2005, Autumn 2006, Autumn 2007, Autumn 2008, Autumn 2010, Autumn 2011, Autumn 2011 - acreditation, Autumn 2012, Autumn 2013, Autumn 2014, Autumn 2015, Autumn 2016, autumn 2017, Autumn 2018, Autumn 2019, Autumn 2020.
  • Enrolment Statistics (Autumn 2009, recent)
  • Permalink: https://is.muni.cz/course/sci/autumn2009/M3150