대한수학회논문집 (Communications of the Korean Mathematical Society)

  • 제26권2호
  • /
  • Pages.163-168
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  • 2011
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  • 1225-1763(pISSN)
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  • 2234-3024(eISSN)
대한수학회 (Korean Mathematical Society)
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LOCALLY-ZERO GROUPOIDS AND THE CENTER OF BIN(X)

  • Fayoumi, Hiba F. (Department of Mathematics University of Alabama)
  • 투고 : 2010.01.07
  • 발행 : 2011.04.30
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초록

In this paper we introduce the notion of the center ZBin(X) in the semigroup Bin(X) of all binary systems on a set X, and show that if (X,${\bullet}$) ${\in}$ ZBin(X), then x ${\neq}$ y implies {x,y}=${x{\bullet}y,y{\bullet}x}$. Moreover, we show that a groupoid (X,${\bullet}$) ${\in}$ ZBin(X) if and only if it is a locally-zero groupoid.

키워드

참고문헌

  1. R. H. Bruck, A Survey of Binary Systems, Springer-Verlag, New York, 1958.
  2. H. S. Kim and J. Neggers, The semigroups of binary systems and some perspectives, Bull. Korean Math. Soc. 45 (2008), no. 4, 651-661. https://doi.org/10.4134/BKMS.2008.45.4.651
  3. L. Nebesky, An algebraic characterization of geodetic graphs, Czechoslovak Math. J. 48(123) (1998), no. 4, 701-710.
  4. L. Nebesky, A tree as a finite nonempty set with a binary operation, Math. Bohem. 125 (2000), no. 4, 455-458.
  5. L. Nebesky, Travel groupoids, Czechoslovak Math. J. 56(131) (2006), no. 2, 659-675.

피인용 문헌

  1. The Interaction between Fuzzy Subsets and Groupoids vol.2014, 2014, https://doi.org/10.1155/2014/246285
  2. Hyperfuzzy subsets and subgroupoids vol.33, pp.3, 2017, https://doi.org/10.3233/JIFS-17104
  3. Fuzzy rank functions in the set of all binary systems vol.5, pp.1, 2016, https://doi.org/10.1186/s40064-016-3536-z
  4. The Hypergroupoid Semigroups as Generalizations of the Groupoid Semigroups vol.2012, 2012, https://doi.org/10.1155/2012/717698
  5. On Abelian and Related Fuzzy Subsets of Groupoids vol.2013, 2013, https://doi.org/10.1155/2013/476057
  6. Fuzzy Upper Bounds in Groupoids vol.2014, 2014, https://doi.org/10.1155/2014/697012
  7. A Method to Identify Simple Graphs by Special Binary Systems vol.10, pp.7, 2018, https://doi.org/10.3390/sym10070297