Coxeter algebras and pre-coxeter algebras in smarandache setting
Hee Sik Kim, Young‐Hee Kim, J. Neggers · Honam Mathematical Journal · 2004
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.