20.500.12556/RUL-103928 Nilpotentne matrike nad antikolobarji Nilpotent matrices over antirings Glavna tema diplomske naloge je opis lastnosti nilpotentnih matrik nad antikolobarji. V prvem poglavju se posvetimo abstraktnim strukturam, natančneje, grupam in polkolobarjem. Pogledamo si bomo lastnosti, ki veljajo za polgrupe, monoide in grupe, nato pa preidemo še na lastnosti polkolobarjev. Nadaljujemo s kratkim opisom zgodovine študije matrik nad polkolobarji ter podamo nekaj definicij in lem, ki jih uporabimo v nadaljevanju. Definiramo, kaj je antikolobar in obravnavamo nilpotentnost elementov in matrik, prav tako definiramo permanento ter z njo povezane permanentne minorje. Sledi poglavje, na katerega se navezuje naslov diplomske naloge, lastnosti nilpotentnih matrik. Nekaj strani namenimo še simultani nilpotenci in nilpotentnemu indeksu. V zadnjem delu pa podamo metodo, s katero ta indeks tudi poiščemo. The main goal of this thesis is to decribe the properties of nilpotent matrices over antirings. We start with the introduction of the abstract structures, more precisely, groups and semirings. We observe the properties that apply to semigroups, monoids and groups, and also the properties that apply to semirings. After a brief description of the history of previous studies done on matrices over semirings, we give some denitions and lemmas that are used later on. We dene what an antiring is and talk about nilpotence of elements and matrices, we also dene the permanent and the associated permanent minors. Next, we dene and describe the properties of the nilpotent matrices. We also write about simultaneous nilpotency and the nilpotent index. At the end we provide a method for calculationg the nilpotent index. antikolobar nilpotentna matrika permanenta permanentni minor digraf simultana nilpotenca nilpotentni indeks. antiring nilpotent matrix permanent permanent minor digraph simultaneously nilpotency nilpotent index. true false false Slovenski jezik Angleški jezik Diplomsko delo/naloga 2018-09-28 12:00:12 2018-09-28 12:00:14 2022-08-17 03:42:16 0000-00-00 00:00:00 2018 0 0 0000-00-00 NiDoloceno NiDoloceno NiDoloceno 0000-00-00 0000-00-00 0000-00-00 1970-01-01 21489 Trojer_Klarisa_-_Nilpotentne_matrike_nad_antikolobarji.pdf Trojer_Klarisa_-_Nilpotentne_matrike_nad_antikolobarji.pdf 1 00FDF4BE3F406892D6F7836281A2B5C5 4d614e8e96591461ea559ade7bbbd257c5778780eb57e258206938b7aba3c78c f06f51af-a1b5-11eb-a523-00155dcfd717 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=114435 Fakulteta za računalništvo in informatiko 0 0 0