High Quality Content by WIKIPEDIA articles! In mathematics, the star product of two graded posets (P,le_P) and (Q,le_Q), where P has a unique maximal element widehat{1} and Q has a unique minimal element widehat{0}, is a poset P * Q on the set (Psetminuswidehat{1})cup(Qsetminuswidehat{0}). We define the partial order le_{P*Q} by xle y if and only if: 1. {x,y}subset P, and xle_P y; 2. {x,y}subset Q, and xle_Q y; or 3. xin P and yin Q. In other words, we pluck out the top of P and the bottom of Q, and require that everything in P be smaller than everything in Q. For example, suppose P and Q are the Boolean algebra on two elements.

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