On Non Commutative Multirings with Involutions

Kaique Ribeiro Santos; Hugo Luiz Luiz Mariano; Kaique Matias de Andrade Roberto

doi:10.20944/preprints202407.2549.v1

Preprint Article Version 1 This version is not peer-reviewed

Version 1 : Received: 30 July 2024 / Approved: 31 July 2024 / Online: 31 July 2024 (14:11:40 CEST)

The primary motivation for this work is to develop the concept of Marshall's quotient (\cite{ribeiro2016functorial}) applicable to non-commutative multirings endowed with involution, expanding the main ideas of the classical (= commutative, without involution) case presented in Marshall's seminal paper \cite{marshall2006real}. We define two multiplicative properties to deal with the involutive case and characterize their Marshall quotient. Besides, this article presents various cases showing that the ''multi'' version of rings with involution offers many examples, applications, and relatives in (multi) algebraic structures.

multirings; involutions; abstract real algebra

Computer Science and Mathematics, Algebra and Number Theory

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On Non Commutative Multirings with Involutions

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