Topics in algebra

2025/2026

Programme:

Doctoral Programme Mathematics and Physics

Orientation:

Mathematics

Year:

1 ali 2 year

Semester:

first or second

Kind:

optional

ECTS:

Language:

slovenian, english

Course director:

Acad. Prof. Dr. Matej Brešar, Prof. Dr. Jakob Cimprič, Prof. Dr. Primož Moravec

Lecturer (contact person):

Assoc. Prof. Dr. rer. nat. Daniel Smertnig, Prof. Dr. Primož Potočnik, Assist. Prof. Dr. Urban Jezernik

Hours per week – 1. or 2. semester:

Lectures

Seminar

Tutorial

Lab

There are no prerequisites.

The content consists of a selection of standard topics in algebra. Possible themes include group theory, commutative algebra, noncommutative algebra, linear algebra, Lie and other nonassociative algebras, universal algebra, ordered algebraic structures etc.
The choice may depend on students' research interests.

N. Dunford, J. T. Schwartz: Linear operators. Part 1, General theory, New York : Interscience Publishers, 197?.
N. Dunford, J. T. Schwartz: Linear operators. Part 2, Spectral theory. Self adjoint operators in Hilbert space, New York : Interscience Publishers, 1967.
N. Dunford, J. T. Schwartz: Linear operators. Part 3, Special operators, New York : Wiley-Interscience, 1971.
L. C. Evans: Partial Differential Equations, Providence : American Mathematical Society, cop. 1998.
L. Grafakos: Classical and Modern Fourier Analysis, Upper Saddle River (NJ) : Pearson Education, cop. 2004.
L. Hörmander: An introduction to complex analysis in several variables, 3. revised ed., Amsterdam : North-Holland, cop. 1990.
T. W. Palmer: Banach algebras and the general theory of *-algebras. Vol. 1, Algebras and Banach algebras, Cambridge : Cambridge University Press, 1994.
R. O. Wells: Differential analysis on complex manifolds, 3rd ed., New York : Springer, cop. 2008.

The main goal of the course is to provide students with some important topics in algebra.

Knowledge and comprehension of presented concepts.
Ability to use acquired knowledge and skills.

Lectures, consultations, problem sessions

Written exam (homeworks), oral exam
grading: 5 (fail), 6-10 (pass) (according to the Statute of UL)

Matej Brešar:
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. Algebras in which non-scalar elements have small centralizers. Linear and Multilinear Algebra, ISSN 0308-1087, 2015, vol. 63, no. 9, str. 1864-1871. [COBISS-SI-ID 17160537]
Jakob Cimprič:
CIMPRIČ, Jaka. A Real Nullstellensatz for free modules. Journal of algebra, ISSN 0021-8693, 2013, vol. 396, str. 143-150. [COBISS-SI-ID 16912729]
CIMPRIČ, Jaka, SAVCHUK, Yurii, SCHMÜDGEN, Konrad. On q-normal operators and the quantum complex plane. Transactions of the American Mathematical Society, ISSN 0002-9947, 2014, vol. 366, no. 1, str. 135-158. [COBISS-SI-ID 16921177]
Primož Moravec:
JEZERNIK, Urban, MORAVEC, Primož. Bogomolov multipliers of groups of order 128. Experimental mathematics, ISSN 1058-6458, 2014, vol. 23, iss. 2, str. 174-180. [COBISS-SI-ID 17109593]
DELIZIA, Constantino, MORAVEC, Primož, NICOTERA, Chiara. Groups with all centralizers subnormal of defect at most two. Journal of algebra, ISSN 0021-8693, 2013, vol. 374, str. 132-140. [COBISS-SI-ID 16556889]
MORAVEC, Primož. Unramified Brauer groups of finite and infinite groups. American journal of mathematics, ISSN 0002-9327, 2012, vol. 134, no. 6, str. 1679-1704. [COBISS-SI-ID 16521305]