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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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The coronation ordines of Charles IV. as ritualized rulers programme
Žůrek, Václav ; Doležalová, Eva (referee) ; Žemlička, Josef (advisor)
The present diploma thesis is an attempt to find new ways of interpreting the Charles IV.'s coronation ordines text (Drdo ad coronandum regem Boemorum). The rudimentary analysis ofthis source was already accomplished by Josef Cibulka and it is precisely his work which served us as a basis. We attempted to take into account the contemporary medievalist literature which deals with coronation and intronization rituals in Europe abundantly. Even though the main topic of the contemporary works are rituals of the early Middle Ages, their conclusions can be helpful for our thesis as well. We have described the situation before Charles IV.' s acceSSlOn, especially the chronichlers' descriptions of the Přemyslid corronations. The analysis of these sources doesn't provide us sufficient information to decide whether a Přemysliďs coronation ordines text existed in the 13th century (surely not before) or not. Basing ourselves on the coronation ordines text analysis we have come to the conclusion that the Czech coronation ordines text was modeled on the ground of the Otonian coronation ordines text from the 10th century and was extended with several elements from the French ordines text from the 13th century which were created during the reign of Saint Louis IX. Beside the French inspiration, the Czech coronation ordines...
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The Magdeburg law in the towns of northwest Bohemia in pre-Hussite period
Mareš, Jan ; Žemlička, Josef (advisor) ; Bobková, Lenka (referee) ; Sulitková, Ludmila (referee)
The beginnings and propagation of the Magdeburg Law in the Czech lands in the Middle Ages are in the centre of attention of historical sciences since the second half of the 19th century. The period of great interest in this theme ends in the middle of the last cen tury and there i s a change in the direction of conservation of older knowledge. A detailed look on notorious development trends in connection with use of different types of sources can open new possibilities for efforts concerning deeper cognition of one of the most important components of the so called medieval transformation. The Magdeburg Law is a phenomenon transgressing borders of contemporary as well as medieval states in Centra!- and Eastern Europe, which is the reason to study it in the context of wider regions. Presented study incorporates three themes. The first chapter is dedicated to the analysis of the initial situation that existed in the thirteenth century in one of the most important cities of northwest Bohemia Litoměřice, the later head of a great family of cities of German town law. The starting point for an attempt to explore the Litoměřice law in the 13th century is a not preserved compilation of various legal regulations sent directly from Magdeburg to Litoměřice in 1282. This is a rare case in Czech lands, which could be...
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Tiliting modules of finite type
Šaroch, Jan ; Žemlička, Jan (referee) ; Trlifaj, Jan (advisor)
The thesis studies properties of cotorsion pairs in the category of modules; we are mostly interested in conditions under which the given cotorsion pair is complete or, actually, of finite type. Methods of deconstruction of cotorsion pairs developed during our inquiry are eventually used to prove that every tilting module is of finite type. We show also a connection of presented problems with so-called telescope conjecture.
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Factorization of polynomials over finite fields
Straka, Milan ; Stanovský, David (referee) ; Žemlička, Jan (advisor)
Nazcv prace: Faktorizace polynoinu nad konccnynii telesy Autor: Milan Straka Katcdra (ustav): Katcdra algebry Vedouci bakalarske prace: Mgr. Jan Zcmlicka, Ph.D. E-mail vedouciho: Jan.Zemlicka((hnff. cuni.cz Abstrakt: Cilem prace je prozkoumat problem rozkladu polynomn nad konecnym telc- scm na soucin ircducibilnich polynoinu. PopHanim nekolika algoritmu hledaji- cich tento rozklad se ukaze, ze tento problem je vzdy fcsitclny v polynornialnim case vzhleclem kc stupni polynomu a poctu prvku konecneho telcsa. U jeduoho z algoritnm je po])sana implenientace s vclnii clobrou asymptotic- kou casovou slozito.sti O(nLylD log c/}, kdc i\. jc stupen rozkladaneho polynuinn nad telesem « q prvky. Program pouzivajiei jcdnodnssi, ale prakticky rychlcjsi variantu tohoto algoritnm jc soucasti ])racc. Klicova slova: faktorizace, kouecna telesa, polynoniy, algoritmns Title: Factoring polynomials over finite fields Author: Milan Straka Department: Department of Algebra Supervisor: Mgr. Jan Zemlicka, Ph.D. Supervisor's e-mail address: Jan. Zcirilicka@mJJ.cum.cz Abstract: The goal of this work is to present the problem of the decomposition of a polyno- mial over a finite field into a product of irreducible polynomials. By describing algorithms solving this problem, we show that the decomposition can always be found in...
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Identity checking
Polach, František ; Žemlička, Jan (referee) ; Stanovský, David (advisor)
Nazev prace: Testovdni identit Autor: FrantiSek Polnch Katedra (ustav): Katedra algebry Vedouci bakalafske prace: RNDr. David Stanovsky, Ph.D. e-mail vedouciho: stanovsk@karlin.mff.citni.cz Abstrakt: Na overeni, zda dana identita (napf. komlttativita, asociativita, apod.) plati v dane algebre (grupe, okrului,...), existuje ocividny algoritmtts, ktery ma exponencidlni slozitost vzh- ledem kdelce zadane identity (profixm'algebru)- Neni tezke nahlednout, ze tento problemje pro libovolnou algebra v I ride co-NP a ze existuji algebry, pro ktere je co-NP-uplny. Na druhou stranu, pro mnoho algeber (napr. pro abelovske grupy) existitje algoritmus polynomidlni. Ex- istuje mezindrodni projekt, jehoz cilein je charakterizovat ty algebry, pro ktere je tento prob- lem pollfnomidlni, rcsp. co-NP-iiplny. Cflem tcto prdceje shrnout nektere zndme vysledky o grupdch a okruzich. Konkretne ukdzeme polynomidlni algoritmy pro testovdni identit v nilpo- tentnich i dihedrdlnfch grupdch a nilpotentnich okruzich, a dokdzeme co-NP-iiplnost testovdni identit v nenilpotcntnfch okruzich. Klicova slova: testovdni identit, slozitost, grupy, okruhy Title: Identity checking Author: Franlisek Polach Department: Department of Algebra Supervisor: RNDr. David Stanovsky, Ph.D. Supervisor's e-mail address: stanovsk@karlin.inff.cuni.cz Abstract:...
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Czech prince and Saxon duke in 12th century. Comparison of the Czech principate and Saxon duchy of Henry the Lion
Zelenka, Jan ; Žemlička, Josef (advisor) ; Bláhová, Marie (referee)
If we resume the results of our comparison, we can see that the basic difference between the duchy of Saxony, territorial domain of Henry the Lion and Bohemian principality is represented by inner political structure of these domains. In consequent this inner political structure were also the chances ofthe emperor encroach diverged. The Saxonian duchy was a conglomerate of major number of aristocratic domains. The holders of these domains (bishops, earls ..... etc.) did not subordinate to fiats of the duke, they did not grant his authority. His power and support from emperor Frederick I. Barbarossa gave him a factual dominance over the other princes of Saxony however it did not let him to beared rule over them. His effort to enlarge his own principality threatened other princes's political positions and that is why they were in constant opposition
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Jindřich Korutanský as Czech king in the light of contemporary testimonies
Razim, Jakub ; Žemlička, Josef (advisor) ; Doležalová, Eva (referee)
Závěrem se sluší zrekapitulovat výsledky, ke kterým nás dovedlo zkoumání pramenů k české I vládě Jindřicha Korutanského v letech 1306 - 131 O. Historický přehled sestavený na jejich základě poukazuje na mimořádně obtížnou pozici, v níž se korutanský vévoda po nástupu na český trůn ocitl. Po celou dobu svého panování musel Jindřich čelit jednak hrozbě zvenčí, ať už to byli Habsburkové, nebo Lucemburkové, jednak domácí opozici tvořenou částí panstva, patriciátu a v první řadě cisterciáckými kláštery. Neměl ani širší podporu ze strany šlechty, a proto byl jeho režim odkázán na vojenské oddíly ze zahraničí, ani potřebné finanční prostředky, takže vojsko hospodařilo na účet obyvatelstva. Výsledkem byla anarchie a nespokojenost s Jindřichovou vládou, kterou ukončil roku 131 O státní převrat.
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The entrapment of the Czech nobility by Pragues and Kutná Hora's patriciate in the year 1309 or else "there is no more harsher man than the ennoblement making ribald". (The entry for patriciate history in 13. and 14. century)
Musílek, Martin ; Žemlička, Josef (advisor) ; Dvořáčková, Dana (referee)
The historical research devoted only small focus on the entrapment of the Czech nobility. Generally, mainly the conclusions made by Josef Šusta had been taken into account. Specialists say that we have no chance to find something new in this subject of historical scholarship. Big deposits of silver were found near Kutná Hora during Václav's II rule. The hot symbiosis started up between the monarch and the tops of the patriciate. This friendship was bringing benefits to both of the sites of the symbiosis. The patriciates was able to do businesses and trades very easily, when the monarch stood by their side. In retum for this the patriciates was providing the valuable services to monarch, especially managing the royal chamber or helping in financial crisis. Helping in financial crisis became important during times of expensive and ambitious statesmanship of the last Přemysls. When the last of the Přemysls died, the prominent patriciates were starting to participate in political events that were shaking the whole kingdom. They were taking part in voting congresses, different missions; actually some of Czech pretendents tried to win the patriciates over. In these years the entrapment of the Czech nobility in Sedlec and in Prague also took place. When we evaluate the previous development, we have the question:...
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Amenities in Czech collegiate chapters in the mid-14th century (on the example of Stará Boleslav, Litoměřice and Vyšehrad)
Pátrová, Karin ; Žemlička, Josef (advisor) ; Doležalová, Eva (referee) ; Bláhová, Marie (referee)
Majetkové zázemí českých kolegiátních kapitul prodělalo od svého vzniku značné proměny. Zpočátku byl kapitulní majetek užíván společně všemi kanovníky, jak naznačují zakládací listiny nejstarších českých kolegiát, v nichž jsou donace adresovány kapitulám jako jednotné instituci. Zatímco o společném soužití kanovníků pod jednou střechou panují určité pochybnosti, svůj majetek získávala kapitula skutečně jako celek. Někdy mohl být zvýhodněn představený kap i tu ly, l když tato praxe již odporovala původním ideálům. Jak kanovníci tento společný majetek užívali, není zcela jasné (zda se scházeli u jednoho stolu, což asi v případě ženatých kanovníků nepřicházelo v úvahu, nebo zda každý kanovník dostával nějaký procentuální podíl). V průběhu 12. a 13. století dochází k výrazným změnám ve skladbě kapitulního majetku a dosud společné jmění je rozděleno mezi jednotlivé kap i tuláry, kteří si své díly sami spravují a užívají jejich výnosy. Z kapitulního zboží se vydělují prebendy jako hmotné zajištění pro jednotlivé kanovníky, vedle toho pak zůstává část zboží nadále ve společném užívání celé kapitulní korporace, které slouží k zabezpečení provozu kostela a jeho výbavě, k vyplácení příspěvku kanovníkům přítomným v kapitulním kostele při bohoslužbách, případně jsou jako tzv. obedience pronajímány jednotlivým členům...
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