论文标题
在局部线性凸度上，概括为交换代数
On local linear convexity generalized to commutative algebras
论文作者
论文摘要
在工作中考虑了一个基于所有元素可逆的基础的实数领域具有身份的交换性代数a。此外，在由A组成的矩阵中，至少有一个非分级。多维复杂空间中线性凸的域的概念及其某些特性被推广到n代数A的笛卡尔产物。
A commutative associative algebra A with an identity over the field of real numbers which has a basis, where all elements are invertible, is considered in the work. Moreover, among matrixes consisting of the structure constants of A, there is at least one that is non-degenerate. The notion of linearly convex domains in the multi-dimensional complex space and some of their properties are generalized to the space that is the Cartesian product of n algebras A. Namely, the separate necessary and sufficient conditions of the local A-linear convexity of domains with smooth boundary in the space are obtained in terms of nonnegativity and positivity of formal quadratic differential form in A, respectively.
