Algebra

Lecturer:

Jan Mareš (gar.)

Tutor:

Jan Mareš (gar.)

Supervisor:

Department of Mathematics

Synopsis:

After an introduction into the set theory standard algebraic structures are dealt with: groups, rings, fields, modules, linear algebras, lattices, Boolean algebras, rings of polynomials over commutative fields.

Requirements:

Syllabus of lectures:

Axiom system for set theory, relations, ordering, equivalence and subvalence of sets, isomorphism of linearly ordered sets, well-ordering, axiom of choice, Zorn's lemma, ordinals and cardinals. Semigroups, groups, cyclic groups, congruences, factorgroupoids, homomorphism, normal subgroups, permutation groups, direct product. Rings, integral domains, fields, congruences, factorrings, homomorphism, ideals, modules, linear algebras, field of quotients, characteristic, prime field, polynomial rings, finite fields. Lattices, complete lattices, ideals, filters, distributive and modular lattices, Boolean algebras.

Syllabus of tutorials:

Study Objective:

nd to introduce them into the methods used in the general algebra.

Study materials:

Povinná

S. Mac Lane, G. Birkhoff: Algebra. Macmillan Com. New York 1968. (Selected chapters.)

Doporučená

R. Solomon: Abstrct Algebra. American Math.Soc. Belmont 2003.

Note:

Time-table for winter semester 2011/2012:

Time-table is not available yet

Time-table for summer semester 2011/2012:

Time-table is not available yet

The course is a part of the following study plans: