Results. Math. 63 (2013), 209–219 c  2011 Springer Basel AG 1422-6383/13/010209-11 published online August 17, 2011 DOI 10.1007/s00025-011-0189-7 Results in Mathematics Smarandache n-Structure on CI -Algebras Arsham Borumand Saeid and Akbar Rezaei Abstract. In this paper, the notions of CI -algebras, Smarandache CI -algebra, Q-Smarandache filters and Q-Smarandache ideals are intro- duced. We show that a nonempty subset F of a CI -algebra X is a Q-Smarandache filter if and only if A(x, y) ⊆ F , which A(x, y) is a Q-Smarandache upper set. Finally, we introduced the concepts of Sma- randache BE-algebra, Smarandache dual BCK-algebra and Smarandache n-structure on CI -algebra. Mathematics Subject Classification (2010). Primary 06F35; Secondary 03G25. Keywords. CI -algebras, BE-algebra, dual BCK-algebra, implication algebra, Smarandache CI -algebra, Smarandache BE-algebra, (Q-Smarandache) Filter, (Q-Smarandache) ideal. 1. Introduction The Smarandache algebraic structures theory was introduced in 1998 by Padilla [11]. In [6], Kandasamy studied of Smarandache groupoids, sub-grou- poids, ideal of groupoids, seminormal sub groupoids, Smarandache Bol grou- poids, and strong Bol groupoids and obtained many interesting results about them. Smarandache semigroups are very important for the study of congru- ences, and they were studied by Padilla [11]. In [5] Jun discussed the Sma- randache structure in BCI -algebras. He introduced the notion of Smarandache (positive implicative, commutative, implicative) BCI -algebras, Smarandache subalgebras and Smarandache ideals and investigated some related properties. Smarandache BL-algebras have been invented by Borumand Saeid et al. [3], and they deal with Smarandache ideal structures in Smarandache BL-algebras.