"nonassociative loop quasigroup multilinear semiring"@en . . . . "2013-12-31+01:00"^^ . . . "The outcome are theoretical results in loop theory, adequately described in the investigator's summary. The output consists of 7 articles in respected international journals and 24 articles in Czech journals (11 of these articles are rather far from the scope of the project). The structure of expenses is not properly explained. Expenses not clearly related to the project are included."@en . "Neasociativita a multilinearita" . . . . "The project is concerned with interactions of nonassociative structures and multilinear algebra, self-correcting codes, cryptography and group theory. We intend to apply various connections of loops to triadditive and tricrossadditive mappings \u2013 some of them classical and some of them new \u2013 to solve several important problems within the theory of conjugacy closed (CC) loops and commutative Moufang loops. We also intend to establish a firmer theoretical basis for the interaction of CC loops with groups and codes, generalizing and explaining thus various constructions of p-local subgroups of the Monster. We anticipate that semirings will find applications in nonassociative structures in the future, and hence a part of our project is to solve several important structural problems in the theory of semirings. In this context we shall also investigate applications of semirings in cryptography. We also plan to investigate A-loops and Moufang loops of odd order."@en . . "Projekt se zab\u00FDv\u00E1 interakcemi neasociativn\u00EDch struktur s\u00A0multiline\u00E1rn\u00ED algebrou, samoopravn\u00FDmi k\u00F3dy, kryptografi\u00ED a teori\u00ED grup. Hodl\u00E1me pou\u017E\u00EDt r\u016Fzn\u00E9 vazby mezi lupami a triaditivn\u00EDmi a trikrosaditivn\u00EDmi zobrazen\u00EDmi \u2013 n\u011Bkter\u00E9 tyto jsou klasick\u00E9, jin\u00E9 nov\u00E9 \u2013 pro vy\u0159e\u0161en\u00ED n\u011Bkolika d\u016Fle\u017Eit\u00FDch otev\u0159en\u00FDch probl\u00E9m\u016F jak v\u00A0teorii konjuga\u010Dn\u011B uzav\u0159en\u00FDch (CC) lup, tak v\u00A0teorii komutativn\u00EDch moufangovsk\u00FDch lup. Chceme tak\u00E9 vytvo\u0159it dostate\u010Dn\u011B obecnou novou teorii, kter\u00E1 by vysv\u011Btlila dosud zn\u00E1m\u00E9 zp\u016Fsoby konstrukce p-lok\u00E1ln\u00EDch podgrup Monstra. Proto\u017Ee po\u010D\u00EDt\u00E1me s\u00A0t\u00EDm, \u017Ee polookruhy budou hr\u00E1t v\u00A0budoucnu v\u00FDznamnou roli v\u00A0neasociativn\u00ED algeb\u0159e, chceme se t\u00E9\u017E v\u011Bnovat \u0159e\u0161en\u00ED d\u016Fle\u017Eit\u00FDch strukturn\u00EDch ot\u00E1zek jejich teorie. V\u00A0t\u00E9to souvislosti se hodl\u00E1me tak\u00E9 v\u011Bnovat mo\u017En\u00FDm kryptografick\u00FDm aplikac\u00EDm. Pl\u00E1nujeme tak\u00E9 studium A-lup a Moufangovsk\u00FDch lup lich\u00E9ho \u0159\u00E1du." . . "GA201/09/0296" . . "2013-06-12+02:00"^^ . "1"^^ . . . "P\u0159\u00EDnosem projektu jsou teoretick\u00E9 v\u00FDsledky v teorii lup, kter\u00E9 jsou adekv\u00E1tn\u011B pops\u00E1ny v \u0159e\u0161itelov\u011B souhrnu. V\u00FDstup sest\u00E1v\u00E1 ze 7 \u010Dl\u00E1nk\u016F v respektovan\u00FDch mezin\u00E1rodn\u00EDch \u010Dasopisech a 24 \u010Dl\u00E1nk\u016F v tuzemsk\u00FDch \u010Dasopisech (11 z t\u011Bchto \u010Dl\u00E1nk\u016F je zna\u010Dn\u011B vzd\u00E1len\u00FDch z\u00E1m\u011Bru projektu). Struktura \u010Derp\u00E1n\u00ED prost\u0159edk\u016F je nejasn\u00E1. Byly uhrazeny i v\u00FDdaje p\u0159\u00EDmo nesouvisej\u00EDc\u00ED s \u0159e\u0161en\u00EDm projektu."@cs . "1"^^ . . "2014-07-01+02:00"^^ . "33"^^ . "2009-01-01+01:00"^^ . "33"^^ . . . "http://www.isvav.cz/projectDetail.do?rowId=GA201/09/0296"^^ . "0"^^ . "Nonassociativity and multilinearity"@en . . .