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2 results

  • Some Properties Associated with Adequate Transversals

  • Xiangjun Kong
  • Journal:
    Canadian Mathematical Bulletin / Volume 54 / Issue 3 / 01 September 2011
    Published online by Cambridge University Press:
    20 November 2018, pp. 487-497
    Print publication:
    01 September 2011
    • Article
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  • In this paper, another relationship between the quasi-ideal adequate transversals of an abundant semigroup is given. We introduce the concept of a weakly multiplicative adequate transversal and the classic result that an adequate transversal is multiplicative if and only if it is weakly multiplicative and a quasi-ideal is obtained. Also, we give two equivalent conditions for an adequate transversal to be weakly multiplicative. We then consider the case when $I$ and $\Lambda $ (defined below) are bands. This is analogous to the inverse transversal if the regularity condition is adjoined.

  • A NEW CONSTRUCTION FOR REGULAR SEMIGROUPS WITH QUASI-IDEAL ORTHODOX TRANSVERSALS

  • Part of
  • XIANGJUN KONG, XIANZHONG ZHAO
  • Journal:
    Journal of the Australian Mathematical Society / Volume 86 / Issue 2 / April 2009
    Published online by Cambridge University Press:
    01 April 2009, pp. 177-187
    Print publication:
    April 2009
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  • In any regular semigroup with an orthodox transversal, we define two sets R and L using Green’s relations and give necessary and sufficient conditions for them to be subsemigroups. By using R and L, some equivalent conditions for an orthodox transversal to be a quasi-ideal are obtained. Finally, we give a structure theorem for regular semigroups with quasi-ideal orthodox transversals by two orthodox semigroups R and L.