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In this paper we define the Smarandache BL-algebra, Q -Smarandache ideal and Q - Smarandache implicative ideal, we obtain some related results. After that by considering the notions of these ideals we determine relationships between ideals in BL-algebra and Q -Smarandache (implicative) ideals of BL-algebra. Finally we construct quotient of Smarandache BL-algebras via MV-algebra and prove some theorems.doi:10.5281/zenodo.2989966 fatcat:bblqa5ortfd7nnuy5fwjrculsi