Completed course Algebra 1.

# Algebra 2

Groups: binary operations, semigroups, monoids, and groups: basic properties and examples, subgroups and cosets, homomorphisms, normal subgroups and quotient groups, introduction to the structure theory of groups, finite abelian groups.

Rings: basic properties and examples, homomorphisms, ideals and quotients rings, field of fractions, principal ideal domains, rings of polynomials in one and several variables.

Fields: finite extensions, algebraic and transcendental elements and extensions, constructible numbers, splitting fields, algebraically closed fields, finite fields.

Vidav: Algebra, DMFA-založništvo, Ljubljana, 2003.

J. Gallian: Contemporary Abstract Algebra, Brooks/Cole, 2013.

I. N. Herstein: Abstract Algebra, John Wiley & Sons, 1999.

S. Lang: Undergraduate Algebra, Springer, 2005.

L. H. Rowen: Algebra. Groups, rings, and fields. A K Peters, 1994.

Students learn basic concepts of algebra that are needed for further study of mathematics. At the same time they learn abstract thinking and rigorous mathematical language. In the tutorial they acquire practical, working knowledge of the area.

Knowledge and understanding: Knowledge and understanding of basic algebraic concepts.

Application: Application of the theory to problem solving.

Reflection: Understanding the theory through applications.

Transferable skills: Transfer of theory into practice.

Lectures, exercises, consultations

Type (examination, oral, coursework, project): 3 midterm exams instead of written exam, written exam, oral exam. Grading: 1-5 (fail), 6-10 (pass) (according to the Statute of UL)

BREŠAR, Matej. Introduction to noncommutative algebra, (Universitext). Cham [etc.]: Springer, cop. 2014. XXXVII, 199 str. ISBN 978-3-319-08692-7. ISBN 978-3-319-08693-4. [COBISS-SI-ID 17143897]

BREŠAR, Matej, ŠPENKO, Špela. Functional identities of one variable. Journal of algebra, ISSN 0021-8693, 2014, vol. 401, str. 234-244. [COBISS-SI-ID 16842329]

BREŠAR, Matej, KLEP, Igor. A local-global principle for linear dependence of noncommutative polynomials. Israel journal of mathematics, ISSN 0021-2172, 2013, vol. 193, iss. 1, str. 71-82. [COBISS-SI-ID 16626521]