Maximal Ideals in a Bicomplex Algebra and Bicomplex Gelfand-Mazur Theorem
arXiv:1504.04486
Abstract
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.
arXiv admin note: text overlap with arXiv:1503.00109