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Regular CA-Groupoids and Cyclic Associative Neutrosophic Extended Triplet Groupoids (CA-NET-Groupoids) with Green Relations

Author

Listed:
  • Wangtao Yuan

    (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

Based on the theories of AG-groupoid, neutrosophic extended triplet (NET) and semigroup, the characteristics of regular cyclic associative groupoids (CA-groupoids) and cyclic associative neutrosophic extended triplet groupoids (CA-NET-groupoids) are further studied, and some important results are obtained. In particular, the following conclusions are strictly proved: (1) an algebraic system is a regular CA-groupoid if and only if it is a CA-NET-groupoid; (2) if ( S , *) is a regular CA-groupoid, then every element of S lies in a subgroup of S , and every ℋ -class in S is a group; and (3) an algebraic system is an inverse CA-groupoid if and only if it is a regular CA-groupoid and its idempotent elements are commutative. Moreover, the Green relations of CA-groupoids are investigated, and some examples are presented for studying the structure of regular CA-groupoids.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:2:p:204-:d:317256
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    Cited by:

    1. 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.

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