Varieties of Algebras
Varieties of Algebras
复制标题
代数种类
DOI：
10.1007/978-1-4757-0163-0_20
复制
发表时间：
1982
期刊：
影响因子：
--
通讯作者：
R. Pierce
中科院分区：
文献类型：
--
作者：
R. Pierce
最后一章回到了域上代数的一般理论。它简要介绍了代数多项式恒等式理论。我们的主要目标是证明阿米特苏尔定理，该定理确立了非交叉积的有限维中心单除代数的存在性。本章主题的选择就是出于这一目标。幸运的是，在阿米特苏尔定理的证明中遇到了许多关于多项式恒等式的有趣结果：阿米特苏尔-莱维茨基定理、中心多项式的存在性以及原始PI代数的卡普兰斯基-阿米特苏尔定理。
This final chapter returns to the general theory of algebras over a field. It provides a brief introduction to the theory of polynomial identities for algebras. Our main goal is to prove Amitsur’s Theorem which establishes the existence of finite dimensional central simple division algebras that are not crossed products. The choice of topics in the chapter is motivated by this objective. Fortunately, many interesting results on polynomial identities are encountered in the proof of Amitsur’s Theorem: the Amitsur—Levitzki Theorem, the existence of central polynomials, and the Kaplansky—Amitsur Theorem on primitivePI-algebras.