Characterization of ideals of rhotrices over a ring and its applications

Kailash M. Patil
Notes on Number Theory and Discrete Mathematics
Print ISSN 1310–5132, Online ISSN 2367–8275
Volume 27, 2021, Number 1, Pages 138—147
DOI: 10.7546/nntdm.2021.27.1.138-147
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Authors and affiliations

Kailash M. Patil
Department of Mathematics, Dharmsinh Desai University
Nadiad, Gujarat 387001, India

Abstract

We define higher order rhotrices over a commutative unital ring S and obtain a ring \mathcal{R}_n(S) of rhotrices of the order n \in \mathbb{N}. We characterize the ideals and maximal ideals of \mathcal{R}_n(S). As a particular case, we record ideals of rhotrix rings over integers and rhotrix algebras over complex plane \mathbb{C}. As an application, we characterize the maximal ideals of the commutative unital Banach algebra \mathcal{R}_n(\mathbb{C}).

Keywords

  • Rhotrix over a ring
  • Unital ring
  • Maximal ideal
  • Banach algebra

2010 Mathematics Subject Classification

  • 15B99
  • 46J20

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Cite this paper

Patil, K. M. (2021). Characterization of ideals of rhotrices over a ring and its applications. Notes on Number Theory and Discrete Mathematics, 27(1), 138-147, doi: 10.7546/nntdm.2021.27.1.138-147.

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