Coordinatization Theorems For Graded Algebras

Canadian mathematical bulletin

关键词: continued fractions;    Diophantine equations;    fundamental units;    simultaneous solutions;   

DOI  :  10.4153/CMB-2002-048-4

学科分类：数学（综合）

来源: University of Toronto Press * Journals Division

【 摘 要 】

In this paper we study simple associative algebras with finite$mathbb{Z}$-gradings. This is done using a simple algebra $F_g$that has been constructed in Morita theory from a bilinear form$gcolon Uimes Vo A$ over a simple algebra $A$. We show thatfinite $mathbb{Z}$-gradings on $F_g$ are in one to onecorrespondence with certain decompositions of the pair $(U,V)$. Wealso show that any simple algebra $R$ with finite$mathbb{Z}$-grading is graded isomorphic to $F_g$ for somebilinear from $gcolon Uimes V o A$, where the grading on $F_g$is determined by a decomposition of $(U,V)$ and the coordinatealgebra $A$ is chosen as a simple ideal of the zero component $R_0$of $R$. In order to prove these results we first prove similarresults for simple algebras with Peirce gradings.

【 授权许可】

Unknown