M3150 Algebra II

Faculty of Science
Autumn 2004
Extent and Intensity
2/2/0. 4 credit(s) (fasci plus compl plus > 4). Recommended Type of Completion: zk (examination). Other types of completion: k (colloquium).
Teacher(s)
prof. RNDr. Radan Kučera, DSc. (lecturer)
doc. Mgr. Michal Kunc, Ph.D. (seminar tutor)
Guaranteed by
doc. RNDr. Libor Polák, CSc.
Department of Mathematics and Statistics - Departments - Faculty of Science
Contact Person: doc. RNDr. Libor Polák, CSc.
Timetable
Mon 10:00–11:50 N21
  • Timetable of Seminar Groups:
M3150/01: Mon 15:00–16:50 UP1, M. Kunc
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
The second term of algebra being a continuation of Algebra I. The knowledge about fields is deepened, lattices and basics of universal algebra are studied. Numerous applications in informatics are presented.
Syllabus
  • Rings and polynomials (ideals, factorrings, fields, skewfields, extensions, finite fields, symmetric polynomials). Lattices (semilattices and lattices - two approaches, modular and distributive lattices, Boolean lattices, representation of finite distributive and Boolean lattices). Universal algebra (subalgebras, homomorphisms, congruences and factoralgebras, products, subdirect products and corresponding decomposition, terms, varieties, free algebras, Birkhoff's theorem, word problems, heterogeneous algebras and coalgebras, applications in theoretical informatcs).
Literature
  • ROSICKÝ, Jiří. Algebra. 2. vyd. Brno: Vydavatelství Masarykovy univerzity, 1994. 140 s. ISBN 802100990X. 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
Assessment methods (in Czech)
Standardní přednáška se cvičením. Písemná zkouška.
Language of instruction
Czech
Further Comments
The course is taught annually.
Listed among pre-requisites of other courses
Teacher's information
http://www.math.muni.cz/~polak
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 2005, Autumn 2006, Autumn 2007, Autumn 2008, Autumn 2009, 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 2004, recent)
  • Permalink: https://is.muni.cz/course/sci/autumn2004/M3150