Maximal Ideals in a Bicomplex Algebra and Bicomplex Gelfand-Mazur Theorem
Functional Analysis
2018-03-12 v3
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.
Keywords
Cite
@article{arxiv.1504.04486,
title = {Maximal Ideals in a Bicomplex Algebra and Bicomplex Gelfand-Mazur Theorem},
author = {Kulbir Singh and Romesh Kumar},
journal= {arXiv preprint arXiv:1504.04486},
year = {2018}
}
Comments
arXiv admin note: text overlap with arXiv:1503.00109