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Volume 12
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Article

On Non-Commutative Multi-Rings with Involution

by
Kaique M. A. Roberto
†,
Kaique R. P. Santos
† and
Hugo Luiz Mariano
*,†
Institute of Mathematics and Statistics, University of São Paulo, Rua do Matão, 1010, São Paulo 05508-090, Brazil
*
Author to whom correspondence should be addressed.
†
The authors contributed equally to this work.
Mathematics 2024, 12(18), 2931; https://doi.org/10.3390/math12182931
Submission received: 29 July 2024 / Revised: 14 September 2024 / Accepted: 18 September 2024 / Published: 20 September 2024
(This article belongs to the Special Issue Algebraic Structures and Graph Theory, 2nd Edition)
Versions Notes

Abstract

The primary motivation for this work is to develop the concept of Marshall’s quotient applicable to non-commutative multi-rings endowed with involution, expanding upon the main ideas of the classical case—commutative and without involution—presented in Marshall’s seminal paper. We define two multiplicative properties to address the involutive case and characterize their Marshall quotient. Moreover, this article presents various cases demonstrating that the “multi” version of rings with involution offers many examples, applications, and relatives in (multi)algebraic structures. Therefore, we established the first steps toward the development of an expansion of real algebra and real algebraic geometry to a non-commutative and involutive setting.
Keywords: multi-rings; involution; abstract real algebra multi-rings; involution; abstract real algebra

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MDPI and ACS Style

Roberto, K.M.A.; Santos, K.R.P.; Mariano, H.L. On Non-Commutative Multi-Rings with Involution. Mathematics 2024, 12, 2931. https://doi.org/10.3390/math12182931

AMA Style

Roberto KMA, Santos KRP, Mariano HL. On Non-Commutative Multi-Rings with Involution. Mathematics. 2024; 12(18):2931. https://doi.org/10.3390/math12182931

Chicago/Turabian Style

Roberto, Kaique M. A., Kaique R. P. Santos, and Hugo Luiz Mariano. 2024. "On Non-Commutative Multi-Rings with Involution" Mathematics 12, no. 18: 2931. https://doi.org/10.3390/math12182931

APA Style

Roberto, K. M. A., Santos, K. R. P., & Mariano, H. L. (2024). On Non-Commutative Multi-Rings with Involution. Mathematics, 12(18), 2931. https://doi.org/10.3390/math12182931

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