On a classification of the integral rings, finite semigroups and RA-loops with the hyperbolic property / Sobre uma classificação dos anéis de inteiros, dos semigrupos finitos e dos RA-loops com a propriedade hiperbólica
AUTOR(ES)
Antonio Calixto de Souza Filho
DATA DE PUBLICAÇÃO
2006
RESUMO
For a given division algebra of a quaternion algebra, we construct and define two types of units of its $\Z$-orders: Pell units and Gauss units. Also, for the quadratic imaginary extensions over the racionals and some fixed group $G$, we classify the algebraic integral rings for which the unit group ring is a hyperbolic group. We also classify the finite semigroups $S$, for which all integral orders $\Gamma$ of $\Q S$ have hyperbolic unit group $\U(\Gamma)$. We conclude with the classification of the $RA$-loops $L$ for which the unit loop of its integral loop ring does not contain a free abelian subgroup of rank two.
ASSUNTO(S)
grupo álgebra dos quatérnios group anel de grupo semigroup teorema de estrutura álgebra de semigrupo hyperbolic group algebraic integers group ring inteiros algébricos unit semigroup algebra structure theorem unidade loop loop grupo hiperbólico semigrupo ordens orders quaternion algebra
