sentences:  Setting formula_91, the homomorphism formula_92 defined by formula_93, induces an isomorphism formula_94.This is the Kimura factorization of formula_17 into a fibred product of its maximal right and left-handed images.Like the Clifford–McLean Theorem, Kimura factorization (or the "Second Decomposition Theorem for skew lattices") was first given for regular bands (that satisfy the middle absorption
  identity, formula_96 ).