Generalized Projections in Zn

We consider the ring ${\mathbb{Z}}_n$ (integers modulo $n$) with the partial order $\leq$' given by $a\le b$ if either $a=b$ or $a\equiv ab(modn)$'. In this paper, we obtain necessary and sufficient conditions for the poset (${\mathbb{Z}}_n,\le$) to be a lattice.