In this paper we introduced Smarandache – 2 – algebraic structure of R-Module namely Smarandache – R-Module. A Smarandache – 2 – algebraic structure on a set N means a weak algebraic structure A0 on N such that there exist a proper subset M of N, which is embedded with a stronger algebraic structure A1, stronger algebraic structure means satisfying more axioms, by proper subset one understands a subset different from the empty set, from the unit element if any, from the whole set. We define

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... andache – R-Module and obtain some of its characterization through Commutative and Bounded BE-Algebras.