In this paper, we offers a new algebraic point of view for DNA molecules and introduce the algebraic system by using the natural operation based on the \Sigma = {A,C, G, T} . We characterize its structure by using the algebraic theory. We show that (L,\oplus,\otimes)is the distribution lattice of rings with identical element. Furthermore,we generalize this result to the W_\rho(V ) , a set which elements simulates the DNA molecules with sticky ends, the element is called an incomplete double stranded molecules consist of mixed DNA molecules with double and single strands.