http://www.multimediaexpo.cz/mmecz/index.php?action=history&feed=atom&title=Modul%C3%A1rn%C3%AD_svaz Modulární svaz - Historie editací 2026-05-15T18:51:12Z Historie editací této stránky MediaWiki 1.16.5 http://www.multimediaexpo.cz/mmecz/index.php?title=Modul%C3%A1rn%C3%AD_svaz&diff=2587240&oldid=prev Sysop: + Aktualizace 2023-05-31T08:07:26Z <p>+ Aktualizace</p> <table style="background-color: white; color:black;"> <col class='diff-marker' /> <col class='diff-content' /> <col class='diff-marker' /> <col class='diff-content' /> <tr valign='top'> <td colspan='2' style="background-color: white; color:black;">← Starší verze</td> <td colspan='2' style="background-color: white; color:black;">Verze z 31. 5. 2023, 08:07</td> </tr><tr><td colspan="2" class="diff-lineno">Řádka 1:</td> <td colspan="2" class="diff-lineno">Řádka 1:</td></tr> <tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div><del class="diffchange diffchange-inline">{{Wikipedia-cs|</del>Modulární <del class="diffchange diffchange-inline">svaz</del>|<del class="diffchange diffchange-inline">700}}</del></div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins class="diffchange diffchange-inline">'''</ins>Modulární <ins class="diffchange diffchange-inline">svazy''' jsou typy [[Svaz (matematika)</ins>|<ins class="diffchange diffchange-inline">svazů]], které nemusejí být distributivní, ale splňují obecnější podmínku tzv. modularity.</ins></div></td></tr> <tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td></tr> <tr><td colspan="2">&nbsp;</td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">== Definice ==</ins></div></td></tr> <tr><td colspan="2">&nbsp;</td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">Svaz (A,∧,∨) se nazývá '''modulární''', platí-li</ins></div></td></tr> <tr><td colspan="2">&nbsp;</td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;"></ins></div></td></tr> <tr><td colspan="2">&nbsp;</td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">1. &lt;big&gt;\(\forall a,b,c \in A, a \geq c :&nbsp; a \wedge(b \vee c) = (a \wedge b) \vee c\)&lt;/big&gt;.</ins></div></td></tr> <tr><td colspan="2">&nbsp;</td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;"></ins></div></td></tr> <tr><td colspan="2">&nbsp;</td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">2. &lt;big&gt;\(\forall a,b,c \in A, a \leq c :&nbsp; a \vee(b \wedge c) = (a \vee b) \wedge c\)&lt;/big&gt;.</ins></div></td></tr> <tr><td colspan="2">&nbsp;</td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;"></ins></div></td></tr> <tr><td colspan="2">&nbsp;</td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">Podmínky 1 a 2 jsou navzájem duální, tzn. platí-li jedna pak platí i druhá.</ins></div></td></tr> <tr><td colspan="2">&nbsp;</td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;"></ins></div></td></tr> <tr><td colspan="2">&nbsp;</td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">== Vlastnosti ==</ins></div></td></tr> <tr><td colspan="2">&nbsp;</td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">{{RIGHTTOC}}</ins></div></td></tr> <tr><td colspan="2">&nbsp;</td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">Každý [[podsvaz]] modulárního svazu je modulární.</ins></div></td></tr> <tr><td colspan="2">&nbsp;</td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;"></ins></div></td></tr> <tr><td colspan="2">&nbsp;</td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">Každý [[distributivní svaz]] je modulární.</ins></div></td></tr> <tr><td colspan="2">&nbsp;</td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;"></ins></div></td></tr> <tr><td colspan="2">&nbsp;</td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">Svaz A je modulární právě tehdy, když žádný jeho [[podsvaz]] není [[izomorfismus|izomorfní]] se svazem '''N&lt;sub&gt;5&lt;/sub&gt;''' (tzv. pentagon).</ins></div></td></tr> <tr><td colspan="2">&nbsp;</td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;"></ins></div></td></tr> <tr><td colspan="2">&nbsp;</td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">== Příklady ==</ins></div></td></tr> <tr><td colspan="2">&nbsp;</td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">Svaz všech [[podprostor]]ů libovolného [[Vektorový prostor|vektorového prostoru]] je modulární.</ins></div></td></tr> <tr><td colspan="2">&nbsp;</td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;"></ins></div></td></tr> <tr><td colspan="2">&nbsp;</td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">Svaz všech [[Normální podgrupa|normálních podgrup]] [[Grupa|grupy]] G je modulární.</ins></div></td></tr> <tr><td colspan="2">&nbsp;</td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;"></ins></div></td></tr> <tr><td colspan="2">&nbsp;</td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">== Související články ==</ins></div></td></tr> <tr><td colspan="2">&nbsp;</td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">* [[Svaz (matematika)|Svaz]]</ins></div></td></tr> <tr><td colspan="2">&nbsp;</td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">* [[Distributivní svaz]]</ins></div></td></tr> <tr><td colspan="2">&nbsp;</td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">* [[Podsvaz]]</ins></div></td></tr> <tr><td colspan="2">&nbsp;</td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">* [[Úplný svaz]]</ins></div></td></tr> <tr><td colspan="2">&nbsp;</td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;"></ins></div></td></tr> <tr><td colspan="2">&nbsp;</td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;"></ins></div></td></tr> <tr><td colspan="2">&nbsp;</td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">{{Článek z Wikipedie}}</ins></div></td></tr> <tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>[[Kategorie:Algebraické struktury]]</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>[[Kategorie:Algebraické struktury]]</div></td></tr> <tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>[[Kategorie:Teorie uspořádání]]</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>[[Kategorie:Teorie uspořádání]]</div></td></tr> </table> Sysop http://www.multimediaexpo.cz/mmecz/index.php?title=Modul%C3%A1rn%C3%AD_svaz&diff=248231&oldid=prev Sysop: 1 revizi 2013-07-25T16:12:10Z <p>1 revizi</p> <table style="background-color: white; color:black;"> <tr valign='top'> <td colspan='1' style="background-color: white; color:black;">← Starší verze</td> <td colspan='1' style="background-color: white; color:black;">Verze z 25. 7. 2013, 16:12</td> </tr></table> Sysop http://www.multimediaexpo.cz/mmecz/index.php?title=Modul%C3%A1rn%C3%AD_svaz&diff=248230&oldid=prev Sysop: 1 revizi 2012-10-23T08:20:30Z <p>1 revizi</p> <p><b>Nová stránka</b></p><div>{{Wikipedia-cs|Modulární svaz|700}}<br /> <br /> [[Kategorie:Algebraické struktury]]<br /> [[Kategorie:Teorie uspořádání]]</div> Sysop