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On L-sub Q-algebras

  • Foundation, algebraic, and analytical methods in soft computing
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Abstract

This paper introduces the concept of L-sub Q-algebras via the notion of L-subsets and Q -algebras. It presents the notions of commutative L-sub Q-algebra, associative L-sub Q-algebra, and faithful L- sub Q-algebra and also the relation between them. For any given non-empty set, it defines a binary operation that it is converted to a Q-algebra and so it shows any nonempty set can be converted to a Q-algebra. Moreover, L-sub Q-algebra is constructed for any given lattice and L-subset. We present the notion of reproduced Q-algebras and reproduced L-sub Q-algebras and also investigate the relation between these concepts. Under some conditions such as faithfulness and associativity of L-subsets, it is tried to convert the L-sub Q-algebra to L -subgroups. The concept of the stabilizer of Q-algebras is introduced based on L-sub Q-algebras and also the Q-algebras are converted to groups via the stabilizer and faithful L-subsets. (hyper)networks.

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Acknowledgements

The authors are very grateful to the referees for the valuable suggestions in obtaining the final form of this paper.

Funding

This work is supported by Foreign Export Program of China 841 (Grant No. DL 2023041002L).

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Authors and Affiliations

  1. Department of Pure Mathematics, Faculty of Mathematics and Computer, Shahid Bahonar University of Kerman, Kerman, Iran

    Arsham Borumand Saeid

  2. Department of Mathematics, University of Payame Noor, Tehran, Iran

    Roohallah Daneshpayeh & Sirus Jahanpanah

  3. School of Mathematics, Northwest University, P. O. Box 710127, Xi’an, China

    Xiao Long Xin

Authors
  1. Arsham Borumand Saeid
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  2. Roohallah Daneshpayeh
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  3. Sirus Jahanpanah
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  4. Xiao Long Xin
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The authors have contributed equally to this paper.

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Correspondence to Arsham Borumand Saeid.

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Saeid, A.B., Daneshpayeh, R., Jahanpanah, S. et al. On L-sub Q-algebras. Soft Comput 28, 12477–12490 (2024). https://doi.org/10.1007/s00500-024-10345-6

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  • DOI: https://doi.org/10.1007/s00500-024-10345-6

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