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Transposition Regular AG-Groupoids and Their Decomposition Theorems

Author

Listed:
  • Yudan Du

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

  • Xiaohong Zhang

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

  • Xiaogang An

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

Abstract

In this paper, we introduce transposition regularity into AG-groupoids, and a variety of transposition regular AG-groupoids (L1/R1/LR, L2/R2/L3/R3-groupoids) are obtained. Their properties and structures are discussed by their decomposition theorems: (1) L1/R1-transposition regular AG-groupoids are equivalent to each other, and they can be decomposed into the union of disjoint Abelian subgroups; (2) L1/R1-transposition regular AG-groupoids are LR-transposition regular AG-groupoids, and an example is given to illustrate that not every LR-transposition regular AG-groupoid is an L1/R1-transposition regular AG-groupoid; (3) an AG-groupoid is an L1/R1-transposition regular AG-groupoid if it is an LR-transposition regular AG-groupoid satisfying a certain condition; (4) strong L2/R3-transposition regular AG-groupoids are equivalent to each other, and they are union of disjoint Abelian subgroups; (5) strong L3/R2-transposition regular AG-groupoids are equivalent to each other and they can be decomposed into union of disjoint AG subgroups. Their relations are discussed. Finally, we introduce various transposition regular AG-groupoid semigroups and discuss the relationships among them and the commutative Clifford semigroup as well as the Abelian group.

Suggested Citation

  • Yudan Du & Xiaohong Zhang & Xiaogang An, 2022. "Transposition Regular AG-Groupoids and Their Decomposition Theorems," Mathematics, MDPI, vol. 10(9), pages 1-20, April.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:9:p:1396-:d:799396
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    References listed on IDEAS

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    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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