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Doctoral Thesis
DOI
https://doi.org/10.11606/T.45.1992.tde-20210729-002956
Document
Author
Full name
Luiz Gonzaga Xavier de Barros
E-mail
Institute/School/College
Knowledge Area
Date of Defense
Published
São Paulo, 1992
Supervisor
Title in Portuguese
Problema do isomorfismo para algebras de loops
Keywords in Portuguese
Teoria Dos Grupos
Abstract in Portuguese
não disponível
Title in English
not available
Abstract in English
Given a loop l and a ring r, the definition of the loop algebra rl is very similar to the definition of a group algebra. If the characteristic of r is not 2 and the loop algebra rl is alternative, we say that l is an r.A. Loop. We have considered the following problem: given the r.A. Loops l and m and an associative ring r, when will the algebra isomorphism rl'APROXIMADAMENTE IGUAL'rm imply the loop isomorphism l'APROXIMADAMENTE IGUAL'm? we have studied the case when r is a field. First, we consider the case r=q, the rational number field and we study a class of r.A. Loops which is determined by q. Then, we extend this result to fields whose characteristic does not divide the order of the loop
 
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Publishing Date
2021-07-29
 
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