On the endomorphism monoids of (uniquely) complemented lattices
George Grätzer, Jiří Sichler · Transactions of the American Mathematical Society · 2000
Let L L be a lattice with 0 0 and 1 1 . An endomorphism φ \varphi of L L is a { 0 , 1 } \{0,1\} -endomorphism , if it satisfies 0 φ = 0 0\varphi = 0 and 1 φ = 1 1\varphi = 1 . The { 0 , 1 } \{0,1\} -endomorphisms of L L form a monoid. In 1970, the authors proved that every monoid M \mathcal M can be represented as the { 0 , 1 } \{0,1\} -endomorphism monoid of a suitable lattice L L with 0 0 and 1 1 . In this paper, we prove the stronger result that the lattice L L with a given