A normal form theorem for lattices completely generated by a subset
George Grätzer, David Kelly · Proceedings of the American Mathematical Society · 1977
For an m \mathfrak {m} -complete lattice L ( m \mathfrak {m} is an infinite regular cardinal) and subset X of L that m \mathfrak {m} -generates L , we prove a Normal Form Theorem for elements of L expressed as polynomials over X . This generalizes a theorem of B. Jónsson in which such a representation is found for the lattice L freely m \mathfrak {m} -generated by a poset X . We also apply this result to free m \mathfrak {m} -products of m \mathfrak {m} -complete lattices.