sentences:  Normal Skew Lattices
  
  As seen above, formula_6 and formula_5 satisfy the identity formula_96.Bands satisfying the stronger identity, formula_145, are called normal.A skew lattice is normal skew if it satisfies
  
  formula_146
  
  For each element a in a normal skew lattice formula_17, the set formula_148 defined by { formula_149} or equivalently {formula_150} is a sublattice of formula_17, and conversely.