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Good congruences on abundant semigroups with multiplicative quasi-adequate transversals

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Abstract

In this paper, some properties of good homomorphic images of abundant semigroups with a multiplicative quasi-adequate transversal are obtained. After that, good congruences on a class of abundant semigroups with such transversals are studied. We characterize the good congruences by using the so-called good congruence triple. Furthermore, we prove that any good congruence on a class of abundant semigroups with such transversals can be constructed by the good congruence triple.

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Authors and Affiliations

  1. Department of Mathematics, Zhejiang Normal University, Jinhua, Zhejiang, 321004, China

    Xiangfei Ni

  2. Department of Mathematics, Lanzhou University, Lanzhou, Ganshu, 730000, China

    Xiangfei Ni & Yanfeng Luo

  3. LongQiao School of Lanzhou Commercial College, Lanzhou, Ganshu, 730000, China

    HaiZhou Chao

Authors
  1. Xiangfei Ni
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  2. Yanfeng Luo
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  3. HaiZhou Chao
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Corresponding author

Correspondence to Xiangfei Ni.

Additional information

Communicated by Thomas E. Hall.

This research was partially supported by the National Natural Science Foundation of China (No. 10571077) and the Youth Foundation of Zhejiang Normal University (No. KYJ06Y09104).

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Ni, X., Luo, Y. & Chao, H. Good congruences on abundant semigroups with multiplicative quasi-adequate transversals. Semigroup Forum 82, 324–337 (2011). https://doi.org/10.1007/s00233-010-9286-2

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  • DOI: https://doi.org/10.1007/s00233-010-9286-2

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