FMF, Mathematical Library, Lj. (MAKLJ)
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Zornova lema in njena uporaba [Elektronski vir]Zupančič, Žiga, matematikV članku je predstavljena Zornova lema in nekaj ekvivalentnih formulacij. Prikazana je njena uporaba v teoriji grup, kjer je dokazano, da lahko homomorfizme iz podgrup Abelovih grup v deljive grupe ... razširimo na celotno Abelovo grupo. V teoriji kolobarjev je s pomočjo Zornove leme pokazano, da vsak kolobar vsebuje maksimalni levi ideal in da je presek vseh praidealov komutativnega kolobarja enak množici vseh nilpotentnih elementov kolobarja. Dokazan je Cohenov izrek in njegova posplošitev. V nadaljevanju je dokazan izrek, ki pravi, da ima vsak neničelni modul nad obsegom bazo. Njegova posledica pravi, da ima vsak vektorski prostor nad poljem bazo. S pomočjo te posledice je pokazano, da v grupi z več kot dvema elementoma obstaja netrivialni avtomorfizem. Primer uporabe v teoriji grafov pa je dokaz izreka, da vsak povezan graf vsebuje vpeto drevo.Source: Matrika [Elektronski vir] : izbrane teme sodobne fizike in matematike. - ISSN 2385-8567 (Letn. 5, št. 2, 2018, 17 str.)Type of material - e-articlePublish date - 2018Language - slovenianCOBISS.SI-ID - 18454873
Author
Zupančič, Žiga, matematik
Topics
matematika |
Zornova lema |
aksiom izbire |
delna urejenost |
linearna urejenost |
maksimalni element |
mathematics |
Zorn lemma |
axiom of choice |
partial ordering |
total ordering |
maximal element
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