of length one. We describe a partial order with a minimal element which does not have the free-extension property. Example 5.4 Suppose F is a field, G is a group, and X is the set of natural numbers with ρ the usual ordering. The set σ = { ( m, m + 1) : m ∈ X } is the arrow set of the Hasse diagram of X hence σ is a G -grading set for X by Theorem 3.8. Suppose there is an element g ∈ G of infinite order. We let φ : σ → G be the function given by φ ( m, m + 1) = g m for all m ∈ X . Then there is a unique homomorphism Φ : ρ → G such that Φ |$_{σ}$ = φ , but this does not determine a grading for I ( X, ρ, F ) since Im Φ is infinite. Therefore I ( X, ρ, F ) does not have the free-extension property even though it satisfies the requirements of [4, Theorem 4]. Acknowledgements A sabbatical appointment supported a visit to the Atlantic Algebra Center of Memorial University in Newfoundland Canada. It is a pleasure to thank the faculty for their hospitality. This paper answers only some of the many fine questions they posed to the author. The author also thanks Martin Erickson of Truman State University and Gene Abrams of the University of Colorado, at Colorado Springs for suggesting improvements to the writing in earlier drafts. References [1] G. Abrams, Groups Gradings and Recovery Results for Generalized Incidence Rings, J. Alg. 164 (1994) 859-875. 19