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Left (Right) Regular and Transposition Regular Semigroups and Their Structures

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  • Xiaohong Zhang

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

  • Yudan Du

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

Abstract

Regular semigroups and their structures are the most wonderful part of semigroup theory, and the contents are very rich. In order to explore more regular semigroups, this paper extends the relevant classical conclusions from a new perspective: by transforming the positions of the elements in the regularity conditions, some new regularity conditions (collectively referred to as transposition regularity) are obtained, and the concepts of various transposition regular semigroups are introduced (L1/L2/L3, R1/R2/R3-transposition regular semigroups, etc.). Their relations with completely regular semigroups and left (right) regular semigroups, proposed by Clifford and Preston, are analyzed. Their properties and structures are studied from the aspects of idempotents, local identity elements, local inverse elements, subsemigroups and so on. Their decomposition theorems are proved respectively, and some new necessary and sufficient conditions for semigroups to become completely regular semigroups are obtained.

Suggested Citation

  • Xiaohong Zhang & Yudan Du, 2022. "Left (Right) Regular and Transposition Regular Semigroups and Their Structures," Mathematics, MDPI, vol. 10(7), pages 1-16, March.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:7:p:1021-:d:776962
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    References listed on IDEAS

    as
    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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    Cited by:

    1. Nan Sheng & Xiaohong Zhang, 2022. "Regular Partial Residuated Lattices and Their Filters," Mathematics, MDPI, vol. 10(14), pages 1-16, July.

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