Symbol length of p-algebras of prime exponent

被引：6

作者：

Chapman, Adam ^{[1
]}

机构：

[1] Tel Hai Coll, Dept Comp Sci, IL-12208 Upper Galilee, Israel

来源：

JOURNAL OF ALGEBRA AND ITS APPLICATIONS | 2017年 / 16卷 / 07期

关键词：

Central simple algebras; p-algebras; symbol length; linkage; homogeneous polynomial forms; quadratic forms; u-invariant;

D O I：

10.1142/S0219498817501365

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We prove that if the maximal dimension of an anisotropic homogeneous polynomial form of prime degree p over a field F with char( F) - p is a finite integer d greater than 1 then the symbol length of p-algebras of exponent p over F is bounded from above by [d-1/p] - 1 and show that every two tensor products of symbol algebras of lengths k and l with ( k + l)p >= d - 1 can be modified so that they share a common slot. For p = 2, we obtain an upper bound of u(F)/2 - 1 for the symbol length, which is sharp when I-q(3) F = 0.

引用

页数：9