COXETER ALGEBRAS AND PRE-COXETER ALGEBRAS IN SMARANDACHE SETTING

  • KIM, HEE SIK (Department of Mathematics Hanyang University) ;
  • KIM, YOUNG HEE (Department of Mathematics Institute for Basic Science Chungbuk National University) ;
  • NEGGERS, J. (Department of Mathematics University of Alabama)
  • Received : 2004.09.11
  • Published : 2004.12.25

Abstract

In this paper we introduce the notion of a (pre-)Coxeter algebra and show that a Coxeter algebra is equivalent to an abelian group all of whose elements have order 2, i.e., a Boolean group. Moreover, we prove that the class of Coxeter algebras and the class of B-algebras of odd order are Smarandache disjoint. Finally, we show that the class of pre-Coxeter algebras and the class of BCK-algebras are Smarandache disjoint.

Keywords

Coxeter algebra;pre-Coxeter algebra;B-algebra;0-commutative

Acknowledgement

Supported by : Chungbuk National University

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