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.
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页码：2545 / 2552
页数：8
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