CZECH TECHNICAL UNIVERSITY IN PRAGUE
STUDY PLANS
2020/2021

# Algebra

Code Completion Credits Range
01ALGE Z,ZK 6 4+1
Lecturer:
Zuzana Masáková (guarantor)
Tutor:
Zuzana Masáková (guarantor)
Supervisor:
Department of Mathematics
Synopsis:

Firstly, the Peano axioms are treated in detail. Elements of the set theory cover only: equivalence and subvalence, the Cantorov-Bernstein theorem, the axiom of choice and equivalent statements, definition of ordinals and cardinals. Further standard algebraic structures are addressed: semigroups, monoids, groups, rings, integral domains, principal ideal domains, fields, lattices. Independent chapters are devoted to divisibility in integral domains and to finite fields.

Requirements:

01LAA2

Syllabus of lectures:

1. Binary relations, equivalence, ordering

2. The Peano axioms for the natural numbers, principle of recursive definition

3. Equivalence and subvalence of sets, the transfinite induction

4. The axiom of choice and equivalent statements

5. Ordinals and cardinals

6. Semigroups, monoids

7. Groups

8. Rings, integral domains, principal ideal domains, fields

9. Divisibility in integral domains

10. Finite fields

11. Lattices

Syllabus of tutorials:
Study Objective:

Knowledge: elements of the set theory - equivalence and subvalence, the axiom of choice and equivalent statements, ordinals and cardinals; basics of algebra - the Peano axioms, monoids, groups, rings, integral domains, principal ideal domains, fields

Skills: using algebraic structures, applying these structures along with some elements of the set theory in other fields of mathematics

Study materials:

Key references:

[1] Mareš J.: Algebra. Úvod do obecné algebry, 3. vydání. ČVUT, Praha, 1999.

Recommended references:

[2] Mac Lane S., Birkhoff G.: Algebra. Springer, New York, 2005.

[3] Lang S.: Algebra. Springer, New York, 2005.

Note:
Time-table for winter semester 2020/2021:
Time-table is not available yet
Time-table for summer semester 2020/2021:
Time-table is not available yet
The course is a part of the following study plans:
Data valid to 2020-09-18
For updated information see http://bilakniha.cvut.cz/en/predmet5357306.html