Maximal ideals in a bicomplex algebra and bicomplex Gelfand-Mazur theorem

被引：2

作者：

Kumar, Romesh ^{[1
]}

Singh, Kulbir ^{[2
]}

机构：

[1] Univ Jammu, Dept Math, Jammu, India

[2] Govt Degree Coll, Dept Math, Jammu, India

来源：

COMPLEX VARIABLES AND ELLIPTIC EQUATIONS | 2022年 / 67卷 / 10期

关键词：

Bicomplex modules; hyperbolic-valued norm; maximal ideals; bicomplex algebra;

D O I：

10.1080/17476933.2021.1934677

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we study the maximal ideals in a commutative ring of bicomplex numbers and then we describe the maximal ideals in a bicomplex algebra. We found that the kernel of a nonzero multiplicative BC-linear functional in a commutative bicomplex Banach algebra need not be a maximal ideal. Finally, we introduce the notion of bicomplex division algebra and generalize the Gelfand- Mazur theorem for the bicomplex division Banach algebra.

引用

页码：2545 / 2552

页数：8

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