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Super rpp semigroups

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Abstract

We study a class of special strongly rpp semigroups, namely, the class of super rpp semigroups. These super rpp semigroups are generalizations of both superabundant semigroups and Clifford semigroups within the class of rpp semigroups. In particular, we prove that a super rpp semigroup is a semilattice of D (l)-simple strongly rpp semigroups. Our result not only generalizes a well-known theorem of Clifford in the class of completely regular semigroups but also strengthens some structure theorems obtained by Ren-Shum for superabundant semigroups which are orthodox. Some special super rpp semigroups are considered and discussed.

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Authors and Affiliations

  1. Department of Mathematics, Jiangxi Normal University, Nanchang, Jiangxi, 330022, People’s Republic of China

    Xiaojiang Guo

  2. Department of Mathematics, Southwest University, Chongqing, 400715, People’s Republic of China

    Yuqi Guo

  3. Department of Mathematics, The University of Hong Kong, Pokfulam Road, Hong Kong (SAR), People’s Republic of China

    K. P. Shum

Authors
  1. Xiaojiang Guo
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  2. Yuqi Guo
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  3. K. P. Shum
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Corresponding author

Correspondence to Xiaojiang Guo.

Additional information

The research of the first author is supported by the NNSF of China (Grant No. 10961014), NSF of China (Grant No. 10961014), the NSF of Jiangxi Province, the SF of Education Department of Jiangxi Province and the SF of Jiangxi Normal University.

The research of the third author is partially supported by a RGC (CUHK) grant (#2160297/05-07).

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Guo, X., Guo, Y. & Shum, K.P. Super rpp semigroups. Indian J Pure Appl Math 41, 505–533 (2010). https://doi.org/10.1007/s13226-010-0030-0

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  • DOI: https://doi.org/10.1007/s13226-010-0030-0

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