On the structure of regular H-cryptogroups

Authors

  • Kar Ping Shum
  • Xiangzhi Kong
  • Yue Ding

Keywords:

The Green-relations, Homomorphisms of H-abundant semigroups, H-cryptogroups

Abstract

We introduce the concepts of Green-relations on H-abundant semigroups. By using the generalized strong semilattice of semigroups, we show that an H-cryptogroup is a regular H-cryptogroup if and only if it is an HG-strong semilattice of completely J-simple semigroups. This result not only extends a known result of Petrich from the class of completely regular semigroups to the class of semi abundant semi groups but also generalizes a well known result of Fountainon superabundant semigroups from the class of abundant semigroups to the class of semiabundant semigroups.

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How to Cite

Shum, K. P., Kong, X., & Ding, Y. (2007). On the structure of regular H-cryptogroups. European Journal of Pure and Applied Mathematics, 1(1), 46–59. Retrieved from https://ejpam.com/index.php/ejpam/article/view/23