A Q- Smarandache Implicative Ideal of Q-Smarandache BH-algebra

In this book, we define the concept of a Q-Smarandache implicative ideal of a Q-Smarandache BH-algebra, a Q-Smarandache implicative ideal with respect to an element of a Q-Smarandache BH-algebra in ordinary. Also, we gave the Q-Smarandache ( positive implictive ideal, translation ideal, commutative ideal, sub-commutative ideal, p-ideal and q-ideal) of a Q-Smarandache BH-algebra firstly, then we restricted these notions on Q-Smarandache implicative BH-algebra and Q-Smarandache medial BH-algebra. We stated and proved some theorems which determine the relationships among these notions and other types of ideals of a Q-Smarandache BH-algebra in ordinary algebra and by some examples. We showed that these notions are different. Also, we considered some properties of a Q- Smarandache implicative ideal of a Q-Smarandache BH-algebra in ordinary algebra and link them with these new notions.