  Let $R$ be a finite commutative ring with identity and $U(R)$ be its group of
units. In 2005, El-Kassar and Chehade presented a ring structure for $U(R)$ and
as a consequence they generalized this group of units to the generalized group
of units $U^{k}\left( R\right) $ defined iteratively as the group of the units
of $U^{k-1}(R)$, with $U^{1}\left( R\right) =U(R) $. In this paper, we examine
the structure of this group, when $R=\mathbb{Z}_{n}.$ We find a decomposition
of $U^{k}\left(\mathbb{Z}_{n}\right)$ as a direct product of cyclic groups for
the general case of any $k$, and we study when these groups are boolean and
trivial. We also show that this decomposition structure is directly related to
the Pratt Tree primes.
