  If a Nakayama algebra is not cyclic, it has finite global dimension. For a
cyclic Nakayama algebra, there are many characterizations of when it has finite
global dimension. In [She17], Shen gave such a characterization using Ringel's
resolution quiver. In [IZ92], the second author, with Zacharia, gave a cyclic
homology characterization for when a monomial relation algebra has finite
global dimension. We show directly that these criteria are equivalent for all
Nakayama algebras. Our comparison result also reproves both characterizations.
In a separate paper we discuss an interesting example that came up in our
attempt to generalize this comparison result to arbitrary monomial relation
algebras [HI19].
