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On Cyclic Associative Semihypergroups and Neutrosophic Extended Triplet Cyclic Associative Semihypergroups

Author

Listed:
  • Minghao Hu

    (Department of Mathematics, Shaanxi University of Science & Technology, Xi’an 710021, China)

  • Xiaohong Zhang

    (Department of Mathematics, Shaanxi University of Science & Technology, Xi’an 710021, China)

Abstract

This paper introduces a new concept called cyclic associative semihypergroup (CA-semihypergroup). The relationships among CA-semihypergroups, Semihypergroups and LA-semihypergroups are studied through some interesting examples. The relationships among various NET-CA-semihypergroups are also studied. The main properties of strong pure neutrosophic extended triplet CA-semihypergroups (SP-NET-CA-semihypergroups) are obtained. In particular, the algorithm of a generated CA-semihypergroup of order tm+n by two known CA-semihypergroups of order m and n is proven, and a CA-semihypergroup of order 19 is obtained by using a Python program. Moreover, it is proven that five different definitions, which can all be used as the definition of SP-NET-CA-Semihypergroup, are equivalent.

Suggested Citation

  • Minghao Hu & Xiaohong Zhang, 2022. "On Cyclic Associative Semihypergroups and Neutrosophic Extended Triplet Cyclic Associative Semihypergroups," Mathematics, MDPI, vol. 10(4), pages 1-30, February.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:4:p:535-:d:745089
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    References listed on IDEAS

    as
    1. Wangtao Yuan & Xiaohong Zhang, 2020. "Regular CA-Groupoids and Cyclic Associative Neutrosophic Extended Triplet Groupoids (CA-NET-Groupoids) with Green Relations," Mathematics, MDPI, vol. 8(2), pages 1-21, February.
    2. Xiaoying Wu & Xiaohong Zhang, 2019. "The Decomposition Theorems of AG-Neutrosophic Extended Triplet Loops and Strong AG-( l , l )-Loops," Mathematics, MDPI, vol. 7(3), pages 1-13, March.
    3. Xiaogang An & Xiaohong Zhang & Yingcang Ma, 2019. "Generalized Abel-Grassmann’s Neutrosophic Extended Triplet Loop," Mathematics, MDPI, vol. 7(12), pages 1-20, December.
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    Cited by:

    1. Yudan Du & Xiaohong Zhang & Xiaogang An, 2022. "Transposition Regular AG-Groupoids and Their Decomposition Theorems," Mathematics, MDPI, vol. 10(9), pages 1-20, April.
    2. Xiaohong Zhang & Yudan Du, 2022. "Left (Right) Regular and Transposition Regular Semigroups and Their Structures," Mathematics, MDPI, vol. 10(7), pages 1-16, March.

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