Izbrana poglavja iz algebre

2022/2023
Program:
Magistrski študijski program 2. stopnje Matematika
Letnik:
1 ali 2 letnik
Semester:
prvi ali drugi
Vrsta:
izbirni
Skupina:
M2
ECTS:
6
Jezik:
slovenski, angleški
Ure na teden – 1. ali 2. semester:
Predavanja
3
Seminar
0
Vaje
2
Laboratorij
0
Vsebina

Izbrane bodo nekatere standardne teme iz algebre. Možna poglavja so teorija grup, komutativna algebra, nekomutativna algebra, linearna algebra, Liejeve in druge neasociativne algebre, homološka algebra, urejene algebrske strukture itd.

Temeljni literatura in viri

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.

Cilji in kompetence

Namen predmeta je seznaniti študente z nekaterimi pomembnimi temami algebre.

Predvideni študijski rezultati

Znanje in razumevanje predstavljenih konceptov.
Sposobnost uporabe pridobljenega znanja in spretnosti.

Metode poučevanja in učenja

Predavanja, konzultacije, reševanje problemov

Načini ocenjevanja

Pisni izpit (domače naloge), ustni izpit

Ocene: 5 (negativno), 6-10 (pozitivno)

Reference nosilca

Matej Brešar:

– 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. 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. 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]
Igor Klep:
HELTON, J. William, KLEP, Igor, VOLČIČ, Jurij. Geometry of free loci and factorization of noncommutative polynomials. Advances in mathematics, ISSN 0001-8708, June 2018, vol. 331, str. 589-626.https://doi.org/10.1016/j.aim.2018.04.007, doi: 10.1016/j.aim.2018.04.007. [COBISS-SI-ID 18416217]
KLEP, Igor, ŠPENKO, Špela, VOLČIČ, Jurij. Positive trace polynomials and the universal Procesi-Schacher conjecture. Proceedings of the London Mathematical Society, ISSN 0024-6115, Dec. 2018, vol. 117, iss. 6, str. 1101-1134.https://doi.org/10.1112/plms.12156, doi: 10.1112/plms.12156. [COBISS-SI-ID 18564185]
HELTON, J. William, KLEP, Igor, MCCULLOUGH, Scott. The tracial Hahn-Banach theorem, polar duals, matrix convex sets, and projections of free spectrahedra. Journal of the European Mathematical Society, ISSN 1435-9855, 2017, vol. 19, iss. 6, str. 1845-1897. http://dx.doi.org/10.4171/JEMS/707, doi: 10.4171/JEMS/707. [COBISS-SI-ID 18057817]

Primož Moravec:
– 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]
– 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]
– 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]

Peter Šemrl:
– 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]
– ŠEMRL, Peter. Invertibility preservers on central simple algebras. Journal of algebra, ISSN 0021-8693, 2014, vol. 408, str. 42-60 [COBISS-SI-ID 16962649]