Advanced Structures in SuperHyper Algebra: Monoids and Ideals

AJOY KANT DAS; Suman Patra; Takaaki  Fujita; Suman Das

doi:10.5269/bspm.76342

AJOY KANT DAS Assistant Professor, Department of Mathematics, ICV-College.
Suman Patra Department of Mathematics Tripua University (A Central University) , AGARTALA –799 022, TRIPURA ; INDIA.
Takaaki Fujita Independent Researcher, Shinjuku, Shinjuku-ku, Tokyo, Japan; t171d603@gunma − u.ac.jp
Suman Das Department of Education (ITEP), NIT West Tripura, Jirania-799046, West Tripura, Tripura, India;

Résumé

This paper delves into the intricate and innovative realm of SuperHyper monoids and their associated ideals, presenting a comprehensive study of their algebraic structures and properties. By integrating the principles of superhyper operations with the foundational aspects of algebra, we develop a generalized monoid framework that adeptly addresses associative and identity properties while managing indeterminate and conflicting information. The paper introduces and formalizes key concepts such as commutativity, idempotency, and homomorphisms within the context of SuperHyper monoids. We also explore the notion of SuperHyper submonoids and ideals, emphasizing their theoretical significance and practical applications. Through rigorous definitions, illustrative examples, and theorems, we highlight the structural coherence and potential of Super- Hyper algebra to extend traditional algebraic boundaries. This work not only contributes to the theoretical advancement of algebraic hyperstructures but also paves the way for future research in handling complex and uncertain mathematical data.

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Bibliographies de l'auteur

Suman Patra, Department of Mathematics Tripua University (A Central University) , AGARTALA –799 022, TRIPURA ; INDIA.

Research Scholar, Department of Mathematics, Tripura University, Agartala-799022, Tripura, India;

Takaaki Fujita, Independent Researcher, Shinjuku, Shinjuku-ku, Tokyo, Japan; t171d603@gunma − u.ac.jp

Independent Researcher, Shinjuku, Shinjuku-ku, Tokyo, Japan

Suman Das, Department of Education (ITEP), NIT West Tripura, Jirania-799046, West Tripura, Tripura, India;

Assistant Professor, Department of Education (ITEP), NIT West Tripura, Jirania-799046, West Tripura, Tripura, India;

Références

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