"Algebraic methods of solved project will deal mostly with the algebraic number theory, especially with the questions of abelian fields and abstract divisor theory. Properties of rings of integers of cyclotomic fields and some of their ideals will be emphasised and , moreover, problems in normal basis of fields extensions will be solved.Applications of theory of divisor and its generalizations will be investigated in commutative ring theory, in partly ordered groups. In analytic number theory we will continue in the development of methods for solving problems in various areas, e.g. general theorems of Tauber type and Fermat numbers which are connected with Artin conjecture. In Abstract analytic number theory we will continue in investigation of asymptotic properties of various subsequences of arithmetical semigroups. Methods for investigation of algebraic properties of sequences will be extended."@en . "10"^^ . . . "1"^^ . . . "0"^^ . "GA201/97/0433" . "Algebraick\u00E9 metody \u0159e\u0161en\u00E9ho projektu se budou p\u0159ev\u00E1\u017En\u011B zab\u00FDvat algebraickou teori\u00ED \u010D\u00EDsel, speci\u00E1ln\u011B ot\u00E1zkami abelovsk\u00FDch t\u011Bles a abstraktn\u00ED teori\u00ED divizor\u016F. D\u016Fraz bude kladen na vlastnosti okruh\u016F cel\u00FDch \u010D\u00EDsel kruhov\u00FDch t\u011Bles a jejich n\u011Bkter\u00FDch ide\u00E1l\u016F a na vy\u0161et\u0159ov\u00E1n\u00ED problematiky norm\u00E1ln\u00ED b\u00E1ze roz\u0161\u00ED\u0159en\u00ED t\u011Bles. Budou vy\u0161et\u0159ov\u00E1ny mo\u017Enosti aplikace teorie divizor\u016F a jejich zobecn\u011Bn\u00ED v komutativn\u00ED teorii okruh\u016F a teorii uspo\u0159\u00E1dan\u00FDch grup a kategorick\u00E9 vlastnosti t\u011Bchto syst\u00E9m\u016F. V analytick\u00E9 teorii \u010D\u00EDsel se bude pokra\u010Dovat v rozvoji metod pro aplikace v oblasti v\u011Bt Tauberova typu a ve vy\u0161et\u0159ov\u00E1n\u00ED vlastnost\u00ED Fermatov\u00FDch \u010D\u00EDsel, souvisej\u00EDc\u00EDch s Artinovou hypot\u00E9zou. V oblasti abstraktn\u00ED analytick\u00E9 teorie \u010D\u00EDsel se budou vy\u0161et\u0159ovat asymptotick\u00E9 vlastnosti r\u016Fzn\u00FDch\u0159ad aritmetick\u00FDch pologrup. Budou rozv\u00EDjeny metody pro vy\u0161et\u0159ov\u00E1n\u00ED algebraick\u00FDch vlastnost\u00ED \u010D\u00EDseln\u00FDch posloupnost\u00ED." . "P\u0159i \u0159e\u0161en\u00ED projektu byly z\u00EDsk\u00E1ny p\u016Fvodn\u00ED v\u00FDsledky. Jsou publikov\u00E1ny z velk\u00E9 \u010D\u00E1sti v mezin\u00E1rodn\u00EDch \u010Dasopisech, byly p\u0159edneseny na \u0159ad\u011B mezin\u00E1rodn\u00EDch konferenc\u00EDch. \u00DAdaje obsa\u017Een\u00E9 v z\u00E1v\u011Bre\u010Dn\u00E9 kart\u011B odpov\u00EDdaj\u00ED v\u00FDsledk\u016Fm. V\u00FDsledky obohacuj\u00ED z\u00E1kladn\u00ED v\u00FDzkum v"@cs . "Algebraic and analytic methods in number theory"@en . "0"^^ . . "Algebraick\u00E9 a analytick\u00E9 metody v teorii \u010D\u00EDsel" . . . . . . . . . . "http://www.isvav.cz/projectDetail.do?rowId=GA201/97/0433"^^ . "10"^^ .