## M3150 Algebra II

Faculty of Science
Spring 2003
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)
doc. RNDr. Libor Polák, CSc. (lecturer)
doc. Mgr. Ondřej Klíma, 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 of Seminar Groups
M3150/01: No timetable has been entered into IS. L. Polák
M3150/02: No timetable has been entered into IS. O. Klíma
M3150/03: No timetable has been entered into IS. O. Klíma
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