대한수학회보 (Bulletin of the Korean Mathematical Society)

  • 제50권3호
  • /
  • Pages.801-809
  • /
  • 2013
  • /
  • 1015-8634(pISSN)
  • /
  • 2234-3016(eISSN)
대한수학회 (Korean Mathematical Society)
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A CONSTRUCTION OF COMMUTATIVE NILPOTENT SEMIGROUPS

  • Liu, Qiong (Department of Mathematics Shanghai University of Electric Power) ;
  • Wu, Tongsuo (Department of Mathematics Shanghai Jiaotong University) ;
  • Ye, Meng (Department of Mathematics Shanghai Jiaotong University)
  • 투고 : 2012.02.25
  • 발행 : 2013.05.31
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초록

In this paper, we construct nilpotent semigroups S such that $S^n=\{0\}$, $S^{n-1}{\neq}\{0\}$ and ${\Gamma}(S)$ is a refinement of the star graph $K_{1,n-3}$ with center $c$ together with finitely many or infinitely many end vertices adjacent to $c$, for each finite positive integer $n{\geq}5$. We also give counting formulae to calculate the number of the mutually non-isomorphic nilpotent semigroups when $n=5$, 6 and in finite cases.

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참고문헌

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