Normal and Canonical Representations in Free Products of Lattices†
H. Lakser · Canadian Journal of Mathematics · 1970
In solving the word problem for free lattices, Whitman [4] showed that free lattices admit canonical representations, that is, of all polynomials over the generating set representing an element of the lattice, the polynomial of shortest length is unique up to commutativity and associativity. These well-defined shortest polynomials have proved very important in analyzing the internal structure of free lattices in detail; see, e.g., [5]. Sorkin [3] proved that the free product of chains also admits canonical representations; these were exploited by Rolf [2]. In the above-mentioned paper, Sorkin also suggested that the free product of two copies of 22 does not admit canonical representations.