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Vychylující moduly nad Gorensteinovými okruhy
Pospíšil, David ; Žemlička, Jan (referee) ; Trlifaj, Jan (advisor)
Let R be a commutative 1-Gorenstein ring. Our main result characterizes all tilting and cotilting R-modules: up to equivalence: they are parametrized by subsets of the set of all prime ideals of height one. More precisely, every tilting (cotilting) R-module is equivalent to some Bass tilting (cotilting) module. This characterization was known in the particular case of Dedekind domains: Chapter 4 contains a new and simpler proof of this fact. Our main result is proved in Chapter 5, while Chapter 6 deals with the cotilting case. In Chapter 4, there is also a proof of the less well-known fact that all finitely generated tilting modules over commutative rings are projective.
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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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