Maximal Ideals in a Bicomplex Algebra and Bicomplex Gelfand-Mazur\n Theorem

2015/04/17 by Kulbir Singh, Singh, Kulbir, Romesh Kumar +1
Mathematics · #Algebraic and Geometric Analysis #Advanced Topics in Algebra

paper · pdf · doi:10.48550/arxiv.1504.04486

Abstract

In this paper we study the maximal ideals in a commutative ring of bicomplex\nnumbers and then we describe the maximal ideals in a bicomplex algebra. We\nfound that the kernel of a nonzero multiplicative BC-linear functional in a\ncommutative bicomplex Banach algebra need not be a maximal ideal. Finally, we\nintroduce the notion of bicomplex division algebra and generalize the\nGelfand-Mazur theorem for the bicomplex division Banach algebra.\n

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