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D.Happel and L.Unger defined a partial order on the set of basic tiltingmodules. We study the poset of basic pre-projective tilting modules over pathalgebra of infinite type. We give an equivalent condition for that this posetis a distributive lattice. We also give an equivalent condition for that adistributive lattice is isomorphic to the poset of basic pre-projective tiltingmodules over a path algebra of representation infinite type.

Distributive lattices and the poset of pre-projective tilting modules