Liejevi homomorfizmi in funkcijske identitete : magistrsko delo
Peršin, Nina, 1981-
V delu obravnavamo problem o Liejevih homomorfizmih, ki ga je leta 1961 postavil I. N. Herstein. Opišemo surjektivni Liejev Homomorfizem iz Liejevega ideala poševno simetričnih elementov algebre z ...involucijo v necentralni Liejev ideal poševno simetričnih elementov praalgebre z involucijo. Ta problem so leta 2001 rešili K.I. Beidar, M. Brešar, M. A. Chebotar in W. S. Martindale 3rd. Kot osnovno sredstvo pri reševanju tega problema je služila teorija funkcijskih identitet, ki se je razvijala v zadnjih petnajstih letih. V začetnih poglavjih magistrskega dela so podani osnovni pojmi iz teorije kolobarjev. Sledi podroben pregled teorije funkcijskih identitet in v tej zvezi teorije t.i. ▫$d$▫-prostih podmnožic kolobarja. V zadnjem poglavju je podan izrek, ki opiše Liejev homomorfizem med določenima Liejevima podalgebrama asociativnih algeber. Osnovna predpostavka je, da je zaloga vrednosti tega Liejevega homomorfizma 9-prosta množica. Sam problem Liejevih homomorfizmov tako prevedemo na problem ▫$d$▫-prostosti.
Type of material - master's thesis
; adult, serious
Publication and manufacture - Maribor : [N. Peršin], 2006
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