On L-sub Q-algebras

This paper introduces the concept of L-sub Q-algebras via the notion of L-subsets and Q -algebras. It presents the notions of commutative L-sub Q-algebra, associative L-sub Q-algebra, and faithful L- sub Q-algebra and also the relation between them. For any given non-empty set, it defines a binary operation that it is converted to a Q-algebra and so it shows any nonempty set can be converted to a Q-algebra. Moreover, L-sub Q-algebra is constructed for any given lattice and L-subset. We present the notion of reproduced Q-algebras and reproduced L-sub Q-algebras and also investigate the relation between these concepts. Under some conditions such as faithfulness and associativity of L-subsets, it is tried to convert the L-sub Q-algebra to L -subgroups. The concept of the stabilizer of Q-algebras is introduced based on L-sub Q-algebras and also the Q-algebras are converted to groups via the stabilizer and faithful L-subsets. (hyper)networks.