The Inclusion Chart for Special Types of Integral Domains

Below is an inclusion chart showing the various inclusions of the algebraic structures of: commutative rings, integral domains, unique factorization domains, principal ideal domains, Euclidean domains, and Fields:

(1)

\begin{align} \quad \mathrm{Commutative \: Rings} \supset \mathrm{Integral \: Domains} \supset \mathrm{UFDs} \supset \mathrm{PIDs} \supset \mathrm{EDs} \supset \mathrm{Fields} \end{align}