Idea Definition o The ideal generated by a subset H will be denoted by id(H), and if H=af, we write id(a) for id(a) we shall call id(a)a principal ideal. o For an order P, a subset A C P is called down-set fx∈ A and y< c imply that y∈AIdeal Definition 1 The ideal generated by a subset H will be denoted by id(H), and if H = {a}, we write id(a) for id(a); we shall call id(a) a principal ideal. 2 For an order P, a subset A ⊆ P is called down-set if x ∈ A and y ≤ x imply that y ∈ A. Yi Li (Fudan University) Discrete Mathematics March 6, 2012 6 / 1