Communications of the Korean Mathematical Society (대한수학회논문집)

Korean Mathematical Society (대한수학회)
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BRACKET FUNCTIONS ON GROUPOIDS

  • Allen, Paul J. (Department of Mathematics University of Alabama) ;
  • Kim, Hee Sik (Research Institute for Natural Sci. Department of Mathematics Hanyang University) ;
  • Neggers, Joseph (Department of Mathematics University of Alabama)
  • Received : 2018.04.04
  • Accepted : 2018.05.31
  • Published : 2019.04.30
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Abstract

In this paper, we introduce an operation denoted by [$Br_e$], a bracket operation, which maps an arbitrary groupoid ($X,{\ast}$) on a set X to another groupoid $(X,{\bullet})=[Br_e](X,{\ast})$ which on groups corresponds to sending a pair of elements (x, y) of X to its commutator $xyx^{-1}y^{-1}$. When applied to classes such as d-algebras, BCK-algebras, a variety of results is obtained indicating that this construction is more generally useful than merely for groups where it is of fundamental importance.

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References

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