论文标题
真实和Quaternionic nullstellensatz的矩阵版本
Matrix versions of real and quaternionic nullstellensatz
论文作者
论文摘要
真正的零stellensatz是实际代数几何形状的经典结果。最近已将其扩展到Alon和Paran的Quaternionic多项式。本文的目的是将其Quaternion -Nullstellensatz扩展到基质多项式。我们还可以从简化真实左派理想的定义的意义上获得对矩阵多项式的真实零stellensatz的改进。我们使用了希尔伯特（Hilbert）的nullstellensatz矩阵版本的证明中的方法，并获得了它们的扩展，并将其扩展到一个轻度的非共同情况和实际情况。
Real Nullstellensatz is a classical result from Real Algebraic Geometry. It has recently been extended to quaternionic polynomials by Alon and Paran. The aim of this paper is to extend their Quaternionic Nullstellensatz to matrix polynomials. We also obtain an improvement of the Real Nullstellensatz for matrix polynomials in the sense that we simplify the definition of a real left ideal. We use the methods from the proof of the matrix version of Hilbert's Nullstellensatz and we obtain their extensions to a mildly non-commutative case and to the real case.
