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2024 | OriginalPaper | Chapter

3. On Absolute-Valued Algebras with Nonzero Central Element

Authors : Alassane Diouf, Mbayang Amar, Oumar Diankha

Published in: Mathematics of Computer Science, Cybersecurity and Artificial Intelligence

Publisher: Springer Nature Switzerland

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Abstract

The chapter delves into the intricate world of absolute-valued algebras, introduced by Ostrowski in 1918. It focuses on algebras with nonzero central elements, exploring their pre-Hilbert space properties, involutions, and classification. The authors prove that these algebras are finite-dimensional and isomorphic to classical algebras under certain conditions, shedding new light on their structure and behavior. The chapter also discusses the implications for third power-associative algebras, providing a valuable contribution to the field of algebraic structures.

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Title: On Absolute-Valued Algebras with Nonzero Central Element
Authors: Alassane Diouf
Mbayang Amar
Oumar Diankha
Publisher: Springer Nature Switzerland
Book: Mathematics of Computer Science, Cybersecurity and Artificial Intelligence
Print ISBN: 978-3-031-66221-8

Electronic ISBN: 978-3-031-66222-5

Copyright Year: 2024
DOI: https://doi.org/10.1007/978-3-031-66222-5_3

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