论文标题
代数的基本定理的扩展
Extensions of the fundamental theorem of algebra
论文作者
论文摘要
在本文中，以代数的著名基本定理及其利用liouville定理的标准证明，我们证明了代数类型的基本定理，用于左（右）的替代性拓扑组合的综合元素和相关元素的综合性和无处不在的元素和非共同的多样性的基本定理结果，并且在左侧（分别为positive of tosement）。本文的主要结果之一的应用是矩阵的特征值的存在，并具有任意有限维复合代数的条目。我们还证明了矩阵的正确特征值的存在，其中包含有限维的实际代数，其中包含复数的副本。
In this paper motivated by the celebrated fundamental theorem of algebra and its standard proof utilizing Liouville's Theorem, we prove the fundamental theorem of algebra type results for both commutative and noncommutative polynomials in the setting of left (resp. right) alternative topological complex algebras whose topological duals separates their elements and that of such real algebras whose centers contain certain copies of complex numbers. An application of one of the main results of the paper is the existence of eigenvalues for matrices with entries from arbitrary finite-dimensional complex algebras. We also prove the existence of right eigenvalues for matrices with entries from finite-dimensional associative real algebras that contain copies of the complex numbers.
