Topics in algebra

2022/2023
Programme:
Doctoral Programme Mathematics and Physics
Orientation:
Mathematics
Year:
1 ali 2 year
Semester:
first or second
Kind:
optional
ECTS:
6
Language:
slovenian, english
Lecturer (contact person):
Hours per week – 1. or 2. semester:
Lectures
2
Seminar
0
Tutorial
0
Lab
0
Content (Syllabus outline)

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.

Readings

I. M. Isaacs, Algebra: A Graduate Course, AMS, 1994.
T. W. Hungerford, Algebra, Springer, 1974.
S. Lang, Algebra, Springer, 2002.
L. H. Rowen: Graduate Algebra: Noncommutative View, AMS, 2008.
J. J. Rotman, Advanced modern algebra, AMS, 2010.

Objectives and competences

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

Intended learning outcomes

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

Learning and teaching methods

Lectures, consultations, problem sessions

Assessment

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

Lecturer's references

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]
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]
Jaka Cimprič:
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]
ŠEMRL, Peter. The optimal version of Hua's fundamental theorem of geometry of rectangular matrices. Memoirs of the American Mathematical Society, ISSN 0065-9266, 2014, vol. 232, no. 1089, str. 1-74. [COBISS-SI-ID 16947545]
Peter Šemrl:
ŠEMRL, Peter. Invertibility preservers on central simple algebras. Journal of algebra, ISSN 0021-8693, 2014, vol. 408, str. 42-60. [COBISS-SI-ID 16962649]
ŠEMRL, Peter. Invertibility preservers on central simple algebras. Journal of algebra, ISSN 0021-8693, 2014, vol. 408, str. 42-60. [COBISS-SI-ID 16962649]