论文标题
差分基质代数的有限分组
Finite Splittings of Differential Matrix Algebras
论文作者
论文摘要
众所周知，中央简单的代数被其中心的合适有限的galois扩展分开。 Juan和Magid在差异基质代数的设置中研究了该结果的同类，其中构建了分裂基质差异代数的Picard-vessiot扩展。在本文中，我们展示了由有限扩展的差分矩阵代数的实例。在某些情况下，我们将差分矩阵代数的有限分裂扩展与其张量力的微不足道联系起来，并在这些情况下表明，差异矩阵代数的顺序将其学位分开。
It is well known that central simple algebras are split by suitable finite Galois extensions of their centers. A counterpart of this result was studied by Juan and Magid in the set up of differential matrix algebras, wherein Picard-Vessiot extensions that split matrix differential algebras were constructed. In this article, we exhibit instances of differential matrix algebras which are split by finite extensions. In some cases, we relate the existence of finite splitting extensions of a differential matrix algebra to the triviality of its tensor powers, and show in these cases, that orders of differential matrix algebras divide their degrees.
