Let $E$ be the set of all nonzero idempotents from the commutative ring $\mathcal{A}$. An atom in $E$ is an element $e$ in that set such that $ef = f$ for some $f \in E$ implies $f = e$. In other words, the atoms are the smallest elements in $E$ with reference to the partial order defined by $g < h$ if $gh = g$.
Here I have considered $\mathcal{A} = Z_{60}$, set of integers modulo $60$ and $E = \{1, 16, 21, 25, 36, 40, 45\}$.
Can anyone please help me here to understand what is Hasse diagram for the set of all nonzero idempotents from the commutative ring $Z_{60}$ and how to draw it?
Or if possible please suggest me any good book or any reference which would help me to understand the Hasse diagram from the level 0?
Thank you.
For general understanding of the Hasse diagram of a partially ordered set, you can check the Wikipedia article on Hasse diagram, or other sources which are certainly available on the web.
Concerning your particular example, notice that an element is below other iff it divides the other.
It may be convenient to fill in the multiplication table of $E \cup \{0\}$, modulo $60$.
If I didn't get it wrong somewhere with the multiplications, it's the following:
From here, with the order as you defined, the Hasse diagram of $E \cup \{0\}$ is the following:
Now to get the diagram of $E$, just ignore $0$.