|
| |
|
| |
|
|
Extension of fields and solvability of algebraic equations
Štíchová, Kateřina ; Stanovský, David (referee) ; Růžička, Pavel (advisor)
Xaxev praee: Hoxsifeni teles a reseni algebraickyeh rovnie Autor: Katerina fit iehova Katedra (ustav): Kafedra algebry Matematicko-fyxikalni f a k u l t y \ Pnixe Vedouoi bakalarske praee: Mgr. Pavel Kuxioka, Ph.I), Kaledra algebry e-mail vedoueiho: Pavel. Huxieka " i n f f . e u n i . e / Abstrakt: V pfedlo/ene praei se x'rnujciiK1 i'rsciii al^rbrairkvrh rovnic di'iilirhu ax pa- trho sT.u])iir a, CJaluisuvr ti'oiii. \i rasli jr po])s;i.n xpusnli rrscni ai^chraickyrh rovnic. s])ocialnr ( 'a.rda.novy vxnrcu. Dale jc nvcdcna rrorir trios, ktcrii jc stavcliniin prvkrin ])ro iiiishxlujici ka pi loin vlasl ni (ialoisovy t.curir, jcv, jc jadrcni t.rt.u prii.cc. I'o- slcdni ka.])itola sc 7a.l)yv;i aplika.ci (JaJoisovy t.coric. konkrctnc nt'n'sit.i'luosti rovnicc pateho stupno v ra.dikalccli. V Tlvodu. ]>ro Aplikaer a. ])rik!ady a jsinc vyeliaxeli lila.vnc xc /.droje ,7 . Vc 2. ka- ])ilolc jsme sc inspirovali f3] a. |0j. v Tcorii rclcs jsnic pou/ili -'2 . Dalo -1. ka.pitola byla. na])s;ina jioinoci 1 Title: Field extensions and solution of algebraic equations Author: Katerina Stiehova Department: I)c])art incut of Algebra Sii]>crvisor: Mj;r, l'a\'el Huxieka. Pli.D Supervisor's e-mail addre>s Pavel.l\u/icka u infi.cuni.cx Abstract: In the ]ji'cseiit \vork \vc s( udy solut ion of general algebraic c(|iiat Jcjns of...
|
|
| |
|
| |
|
| |
|
| |
|
| |
|
| |
|
|
Abelian regular rings
Vejnar, Benjamin ; Růžička, Pavel (referee) ; Žemlička, Jan (advisor)
Na/ev praco: Abelovsky regularni okruhy Autor: Benjamin Vejnar Katedra (listav): Katedra algebry VcdoLici bakalafske prace: Mgr. Jan 2emlicka, Ph.D. E-mail vedouctho: Jan.Zcmlicka&mJJ. cuni.cz Abstrakt: V pfcdloxene praci studujeme aritmeticke a strukturni vlastnosti abelovsky regularnich okruhu, tedy okruhu, jcjichx ka/xly levy i pravy konecne generova.ny ideal jo generovan idempotentnim prvkem, klery Ic/i v centra danoho okruhu. Napfiklad ka/,dy Boohmv okruh je abelovsky regularni. Venujume ye podininkam, ktere uplne diarakterizuji tn'du abelovsky regu- larnieli okruhu, jako napfiklad silna regularita. Vsimame si souvislosti mexi Booleovou algebrou vsch centralnich idempo1,entu daneho okruhu a hlavnimi idealy. Dale popiHUJeme topologit na nmo/ine visecli prvoidealu a avcdoniujeine si, '/e splyva s Lo])ologii ultrafiltrii na Booleove algebre idciiipotontd. Klicova slova: okruhy, idempoteiitni prvky, silne regularni okruhy Title: Abelian regular rings Author: Benjamin Vejnar Department: Department of Algebra Supervisor: Mgr. Jan Zemlieka, Ph.D. Supervisor's e-mail address: Jan.Zc:ttilicka((})'niff.cu'iii.cz Abstract: In the present work we study arithmetic and structural properties of abelian regular' rings. This means rings whose every left and right finitely generated ideal is generated by an idempotent...
|
guest ::
RSS feed.