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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...
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