Communications of the Korean Mathematical Society (대한수학회논문집)

Korean Mathematical Society (대한수학회)
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ABUNDANT SEMIGROUPS WITH QUASI-IDEAL S-ADEQUATE TRANSVERSALS

  • Kong, Xiangjun (SCHOOL OF MATHEMATICS AND STATISTICS LANZHOU UNIVERSITY) ;
  • Wang, Pei (SCHOOL OF COMPUTER SCIENCE QUFU NORMAL UNIVERSITY)
  • Received : 2010.01.11
  • Published : 2011.01.31
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Abstract

In this paper, the connection of the inverse transversal with the adequate transversal is explored. It is proved that if S is an abundant semigroup with an adequate transversal $S^o$, then S is regular if and only if $S^o$ is an inverse semigroup. It is also shown that adequate transversals of a regular semigroup are just its inverse transversals. By means of a quasi-adequate semigroup and a right normal band, we construct an abundant semigroup containing a quasi-ideal S-adequate transversal and conversely, every such a semigroup can be constructed in this manner. It is simpler than the construction of Guo and Shum [9] through an SQ-system and the construction of El-Qallali [5] by W(E, S).

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Acknowledgement

Supported by : National Natural Science Foundation of China, Natural Science Foundation of Shandong Province

References

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  2. Good congruences on abundant semigroups with $$PSQ$$ P S Q -adequate transversals vol.89, pp.2, 2014, https://doi.org/10.1007/s00233-014-9584-1
  3. The product of quasi-ideal adequate transversals of an abundant semigroup vol.83, pp.2, 2011, https://doi.org/10.1007/s00233-011-9309-7