A completely distributive lattice is also called a molecular lattice.The least and the greatestelements in a lattice are denoted by 0 and 1,respectively.For the empty subset L of alattice L,we assume that V=0 and ∧=1...A completely distributive lattice is also called a molecular lattice.The least and the greatestelements in a lattice are denoted by 0 and 1,respectively.For the empty subset L of alattice L,we assume that V=0 and ∧=1.The set of all the molecules（i.e.non-zero∨-irreducible elements）in a lattice L is denoted by M（L）. Let L<sub>1</sub> and L<sub>2</sub> be completely distributive lattices,f:L<sub>1</sub>→L<sub>2</sub> and g:L<sub>2</sub>→L<sub>1</sub> be order-preserving maps.If for any a∈L<sub>1</sub> and any b∈L<sub>2</sub>,f（a）≤b if and only if a≤g（b）,then fis called the left adjoint of g,or g is called the right adjoint of f.The right adjoint of f展开更多
文摘A completely distributive lattice is also called a molecular lattice.The least and the greatestelements in a lattice are denoted by 0 and 1,respectively.For the empty subset L of alattice L,we assume that V=0 and ∧=1.The set of all the molecules（i.e.non-zero∨-irreducible elements）in a lattice L is denoted by M（L）. Let L<sub>1</sub> and L<sub>2</sub> be completely distributive lattices,f:L<sub>1</sub>→L<sub>2</sub> and g:L<sub>2</sub>→L<sub>1</sub> be order-preserving maps.If for any a∈L<sub>1</sub> and any b∈L<sub>2</sub>,f（a）≤b if and only if a≤g（b）,then fis called the left adjoint of g,or g is called the right adjoint of f.The right adjoint of f
