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On Extendibility of Evolution Subalgebras Generated by Idempotents

Author

Listed:
  • Farrukh Mukhamedov

    (Department of Mathematical Sciences, College of Science, United Arab Emirates University, Al-Ain 15551, United Arab Emirates)

  • Izzat Qaralleh

    (Faculty of Science, Tafila Technical University, P.O. Box 179, Tafila 66110, Jordan)

Abstract

In the present paper, we examined the extendibility of evolution subalgebras generated by idempotents of evolution algebras. The extendibility of the isomorphism of such subalgebras to the entire algebra was investigated. Moreover, the existence of an evolution algebra generated by arbitrary idempotents was also studied. Furthermore, we described the tensor product of algebras generated by arbitrary idempotents and found the conditions of the tensor decomposability of four-dimensional S -evolution algebras. This paper’s findings shed light on the field of algebraic structures, particularly in studying evolution algebras. By examining the extendibility of evolution subalgebras generated by idempotents, we provide insights into the structural properties and relationships within these algebras. Understanding the isomorphism of such subalgebras and their extension allows a deeper comprehension of the overall algebraic structure and its behaviour.

Suggested Citation

  • Farrukh Mukhamedov & Izzat Qaralleh, 2023. "On Extendibility of Evolution Subalgebras Generated by Idempotents," Mathematics, MDPI, vol. 11(12), pages 1-18, June.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:12:p:2764-:d:1174137
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    References listed on IDEAS

    as
    1. Julio Becerra & María Beltrán & M. Victoria Velasco, 2020. "Pulse Processes in Networks and Evolution Algebras," Mathematics, MDPI, vol. 8(3), pages 1-20, March.
    2. Miguel D. Bustamante & Pauline Mellon & M. Victoria Velasco, 2020. "Determining When an Algebra Is an Evolution Algebra," Mathematics, MDPI, vol. 8(8), pages 1-14, August.
    3. M. Eugenia Celorrio & M. Victoria Velasco, 2019. "Classifying Evolution Algebras of Dimensions Two and Three," Mathematics, MDPI, vol. 7(12), pages 1-25, December.
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    1. Farrukh Mukhamedov & Izzat Qaralleh, 2021. "On S -Evolution Algebras and Their Enveloping Algebras," Mathematics, MDPI, vol. 9(11), pages 1-23, May.

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