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\usepackage[czech]{babel} \usepackage[IL2]{fontenc}

\usepackage[mathscr]{eucal} \usepackage{amsfonts, amssymb, amsmath} %\usepackage[T1]{fontenc} \usepackage{makeidx} %\usepackage{showidx}


%VZOROVE SOUBORY

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\newcommand{\qlq}[1]{\qquad\ldots\qquad} %navazani definice \newcommand{\qlr}[3]{\ensuremath{\left#1{#3}\right#2}} %velka ohraniceni vyrazu \newcommand{\qlb}[1]{\ensuremath{\left({#1}\right)}} %velka ohraniceni vyrazu \newcommand{\qz}[1]{\par {\footnotesize\sf #1}\x\\ } %odstavec malym pismem \newcommand{\qe}[2]{\te{equation}{\label{#1}#2}} %vysazeny vzorec \newcommand{\qq}[1]{$${#1}$$} %vysazeny vzorec s implicitnim navestim \newcommand{\qu}[1]{\qquad\left| #1\right.} %prikaz v mat. protredi pro upravu rovnice \newcommand{\mo}[1][]{\raisebox{1ex}{\scriptsize o}#1} %stupne ... \newcommand{\ttitle}[1]{\te{center}{\LARGE\sf {#1}}} \newcommand{\ttab}[1]{\te{tabbing}{{#1}}} %tabulka \newcommand{\tcal}[1]{$\mathcal{#1}$} %caligraficke pismo v textu \newcommand{\tbf}[1]Šablona:\bf %tucne \newcommand{\tit}[1]Šablona:\it %kurziva \newcommand{\trm}[1]Šablona:\rm %normalne \newcommand{\tulsl}[1]{\tul{\sl{#1}}} %podtrzena kurziva \newcommand{\tul}[1]{\underline{#1}} %podtrzene \newcommand{\tuul}[1]{\tul{\tul{#1}}} %dvojte podtryene \newcommand{\tsc}[1]Šablona:\sc %kapitalky \newcommand{\tsf}[1]Šablona:\sf %grotesk \newcommand{\tsl}[1]Šablona:\sl} %textove pole \newcommand{\tram}[2][]{\te{tabular}{[#1]{|l|}\hline {#2} \\\hline}} %ramecek \newcommand{\trram}[2][]{\te{tabular}{[#1]{||l||}\hline\hline {#2} \\\hline\hline}} %dvojity ramecek \newcommand{\ttram}[2][]{\te{tabular}{[#1]{|p{.98\textwidth}|}\hline {#2} \\\hline}} %ramecek na sirku strany \newcommand{\ttrram}[2][]{\te{tabular}{[#1]{||p{.98\textwidth}||}\hline\hline #2 \\\hline\hline}} %dvojity ramacek na sirku strany \newcommand{\mb}[1]{$\displaystyle {#1}$} \newcommand{\mab}[1]{\tam{$\displaystyle {#1}$}} \newcommand{\mrab}[1]{\fbox{$\displaystyle {#1}$}} \newcommand{\tvers}[1]{\te{verse}{#1}} %vers \newcommand{\tenum}[1][1]{\addtocounter{tenumcounter}{#1} \arabic{tenumcounter}} %+radova cislovka \newcommand{\tenumset}[1][0]{\setcounter{tenumcounter}{#1} \arabic{tenumcounter}} %radova cislovka \newcommand{\tuv}[1]{\uv{{#1}}} %ceske uvozovky \newcommand{\tnR}[1]{\setcounter{myowncounter}{#1}\Roman{myowncounter}} %velka rimska cislovka \newcommand{\tna}[1]{\setcounter{myowncounter}{#1}\arabic{myowncounter}} %radova cislovka \def\tc#1Šablona:\Large\sf \newcommand{\mm}[1]{\mathrm{#1}} %text ve vzorci \newcommand{\mder}[2]{\frac{\md #1}{\md #2}} %derivace \newcommand{\mint}[2]{\int#1\,\md#2} %integral \newcommand{\overfrown}[1]{\stackrel{\frown}{{#1}}} \newcommand{\mintu}[4]{\int\limits_{#1}^{#2}#3\,\md#4} %urcity integral \newcommand{\sbod}[1]{{\x ---\x{#1}}\\} \newcommand{\mui}[1]{\ensuremath{^\mathrm{#1}}} \newcommand{\mdi}[1]{\ensuremath{_\mathrm{#1}}} \newcommand{\alphitem}[1]{\addtocounter{alphlistcounter}{1}\alph{alphlistcounter} & \te{minipage}{[t]{.95\textwidth}{#1}} \\[1ex]} \newcommand{\alphlist}[1]{\setcounter{alphlistcounter}{0}\te{tabular}{{r@{)\kern1em}l} #1 }} \newcommand{\tss}{\kern0.3em} \newcommand{\tsm}{\kern0.6em} \newcommand{\tsb}{\kern0.9em} \newcommand{\tabl}{\\\hline} \newcommand{\parag}[1]{\paragraph{{#1}}\setlength{\itsmyownlength}{\parindent}\addtolength{\itsmyownlength}{-0.8ex}\x\\\rule{\itsmyownlength}{0ex}}


%Fyzikalni olympiada \newcommand{\hlavicka}[9]{\te{tabular}{{ll}Jm?no a p??jmen? : {\bf #1} & Ro?n?k: {\bf #6} \\ ?kola: {\bf #2} & ?loha: {\bf {#7}-{#8}-{#9}} \\ {\bf #3} & Posudek:\\ T??da: {\bf #4}\\ Vyu?uj?c? fyziky: {\bf #5} & Posuzoval:}\\[1ex]\hlinefill\\[1ex]} \newcommand{\zadani}[2]Šablona:\it \sc \def\theorem{\numberedpar{Věta}} \def\observation{\numberedpar{Pozorování}} \def\lemma{\numberedpar{Lemma}} \def\remark{\numberedpar{Poznámka}} \def\consequence{\numberedpar{Důsledek}} \def\proof{\paragraph{\raise .2ex \hbox to 0pt{\kern-3ex $\circ$}\it Důkaz.}}

\def\removepar#1\par{\relax}

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\long\def\nothing#1{\relax}

\def\xy#1#2{\relax}

\def\xxy#1#2{ \refstepcounter{subsection} \refstepcounter{section} \addcontentsline{toc}{section}{\numberline{\thesection.} #2} \subsection*{ \hglue -1ex \hbox to 0pt{\rule[3ex]{\textwidth}{1pt}} \hfil {{\rm\large\bfseries\thesection.} {\rm\large\scshape #1}} \hfil} }

\def\xxxy#1#2{ \refstepcounter{subsection} \addcontentsline{toc}{subsection}{\numberline{\thesubsection.} #2} \subsubsection*{ \hglue -1ex \hbox to 0pt{\kern-3.7ex$\bullet$} \hfil {{\rm\normalsize\bfseries\thesubsection.} {\rm\normalsize\scshape #1}} \hfil} }

\def\pp#1{\paragraph{#1.}}

\def\xx#1{\xy{#1}{#1}} \def\xxx#1{\xxy{#1}{#1}} \def\xxxx#1{\xxxy{#1}{#1}}

\def\QED{~\\\rightline{$\Box$}} \newlength{\PARSKIP} \def\QED{\setlength{\PARSKIP}{\parskip}\setlength{\parskip}{-2ex} \hbox{}\allowbreak\hfill %\hbox{}\allowbreak\hfill {$\Box$}\par

\setlength{\parskip}{\PARSKIP}}

\def\cldc{,\ldots,} %comma \ldots coma \def\PP#1{\mathfunction{\mathscr P}\left({#1}\right)} %potence set \def\UU{{\mathcal{U}}} %universum \let\AA=\forall %forall \let\EE=\exists %exists \def\abs#1{\left|{#1}\right|} %absolute value \def\Limpl{\Rightarrow} % short implication \def\Lequiv{\Leftrightarrow} % short logical equivalence \def\equivs{\;\;\Longleftrightarrow\;\;} % short logical equivalence \def\Land{\wedge} % logical and \def\Lor{\vee} % logical or \def\TEXTREL#1{\mathrel{\text{#1}}} \def\Tor{\TEXTREL{vel}} \def\Tand{\TEXTREL{et}} \def\Tnot{\TEXTREL{non}} \def\SET#1#2{\left\{{#1}\divides{#2}\right\}} \def\set#1#2{\left\{#1\left.\vphantom{#2}\vphantom{#1}\right|#2\right\}} \def\anglevector#1{\left\langle{#1}\right\rangle} \def\anglecouple#1#2{\anglevector{#1,#2}} \def\map#1#2#3{#1:#2\rightarrow#3} \def\maptype#1#2#3#4{#1:#2\stackrel{\text{#3.}}{\longrightarrow}#4} \def\matrixtwo#1#2#3#4{\left({#1\atop#3}{#2\atop#4}\right)} \def\1Šablona:-1 \let\sse=\subseteq \let\ssn=\varsubsetneq \def\C{\mathbb{C}} \def\N{\mathbb{N}} \def\Q{\mathbb{Q}} \def\R{\mathbb{R}} \def\Z{\mathbb{Z}} \def\bbA{\mathbb{A}} \def\Nz{\mathbb{N}_0} \def\bbP{\mathbb{P}} \def\calU{\mathcal{U}} \def\calR{\mathcal{R}} \def\calF{\mathscr{F}} \def\calS{\mathcal{S}} \def\calB{\mathcal{B}} \def\calA{\mathcal{A}} \def\divides{\mathop{\mid}} \def\pS#1{\mathscr{S}_{#1}} % permutation group \def\pA#1{\mathscr{A}_{#1}} % even permutation group \def\pp#1#2{\mathscr{#1}_{#2}} \def\ord{\mathfunction{ord}} \def\mathdef{\mathfunction{def}} \let\sm=\smallsetminus % set minus \let\pce=\preccurlyeq % subvalention \let\pna=\precnapprox % sharp subvalention \let\nsg=\vartriangleleft % normal sup-group \let\sg=\Subset % normal sup-group \def\supdot{^\bullet} %\def\sublin{_{\mathrm{lin}}} \def\sublin{_\lambda} \def\subnat{_{\text{nat}}} \def\hatn#1{\widehat{#1}} \def\factorset#1{\mathop{/}{#1}} \def\intpart#1{\left\lfloor#1\right\rfloor} \def\sgn{\mathfunction{sgn}} \def\ditem#1{\item[{\small\bfseries(#1)}]} \def\ch{\mathfunction{ch}} \def\ker{\mathfunction{ker}} \let\rarr=\rightarrow \def\AM#1{\mathscr{A}_{#1}} \def\LM#1{\mathscr{L}_{#1}} \def\KM#1{\mathscr{K}_{#1}} \def\IM#1{\mathcal{I}_{#1}} \def\UM#1{\mathcal{U}_{#1}} \def\EM#1{\mathcal{E}_{#1}} \def\FM#1{\mathscr{F}_{#1}} \def\NM#1{\mathscr{N}_{#1}} \def\MM#1{\mathscr{M}_{#1}} \def\NfŠablona:\NM5 \def\MfŠablona:\MM5 \def\AL#1{\alpha_{#1}} \def\EKŠablona:\EH H \def\id{\mathfunction{id}} \def\lcm{\mathop{\nu}} \def\gcd{\mathop{\delta}} \def\HE#1{\mathrel{_{#1}\mathord\equiv}} \def\EH#1{\mathrel{\mathord\equiv_{#1}}} \def\subplus{_+} \def\subdot{_\bullet} \def\subast{_*} \def\PzeroŠablona:\rm\theta \let\Pz=\Pzero \let\SV=\lor \let\SA=\land \let\CO=\complement \def\st{\mathfunction{st}} \let\ol=\overline \def\RE{\mathfunction{Re}} \def\GF{\mathfunction{\mathrm{GF}}} %\long\def\proof#1\QED{\relax}

\def\labelenumi{{\small \bfseries{(\theenumi)}}}

\title{Zápisky z~Algebry} \author{Tomáš Hejda}