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Maximal ideals in a bicomplex algebra and bicomplex Gelfand–Mazur theorem
Complex Variables and Elliptic Equations ( IF 0.6 ) Pub Date : 2021-06-30 , DOI: 10.1080/17476933.2021.1934677 Romesh Kumar 1 , Kulbir Singh 2
中文翻译:
双复代数中的极大理想和双复 Gelfand-Mazur 定理
更新日期:2021-06-30
Complex Variables and Elliptic Equations ( IF 0.6 ) Pub Date : 2021-06-30 , DOI: 10.1080/17476933.2021.1934677 Romesh Kumar 1 , Kulbir Singh 2
Affiliation
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 -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.
中文翻译:
双复代数中的极大理想和双复 Gelfand-Mazur 定理
在本文中,我们研究了双复数交换环中的极大理想,然后描述了双复代数中的极大理想。我们发现非零乘法的核- 可交换双复数 Banach 代数中的线性泛函不必是极大理想。最后,我们介绍了双复除法代数的概念,并将 Gelfand-Mazur 定理推广到双复除法 Banach 代数。