交换代数中的σ-单原函数

Q3 Mathematics

Proceedings of the International Geometry Center Pub Date : 2023-05-04 DOI:10.15673/tmgc.v16i1.2421

Vitalii Shpakivskyi

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引用次数: 0

摘要

在有限维交换关联代数中，引入了σ-单基因函数的概念。建立了σ-单性的充分必要条件。在一些低维代数中，在σ的特殊选择下，用复变量的全纯函数得到了σ-单基因函数的表示。提出了二维双调和代数中有值的σ-单基因函数在二维双调和方程解表示中的应用。

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σ-monogenic functions in commutative algebras

In finite-dimensional commutative associative algebra, the concept of σ-monogenic function is introduced. Necessary and sufficient conditions for σ-monogeneity have been established. In some low-dimensional algebras, with a special choice of σ, the representation of σ-monogenic functions is obtained using holomorphic functions of a complex variable. We proposed the application of σ-monogenic functions with values in two-dimensional biharmonic algebra to representation of solutions of two-dimensional biharmonic equation.

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来源期刊

Proceedings of the International Geometry Center Mathematics-Geometry and Topology

CiteScore

1.00

自引率

0.00%

发文量

审稿时长

3 weeks