%%group 5

\node[name=rat, right of= proint, NobleGas] {\NaturalElementTextFormat{$0$}{global}{$\mathbb{Q}$}{Rational numbers}}; \node[name=integer, above of =rat, Element] {\NaturalElementTextFormat{$0$}{\phantom{0}}{$\mathbb{Z}$}{Integers}}; \node[name=nat0, above of=integer, Metal] {\NaturalElementTextFormat{$0$}{\phantom{0}}{$\mathbb{N}_{0}$}{Natural numbers}};

\node[name=real, below of=rat, NobleGas] {\NaturalElementTextFormat{$0$}{local}{$\mathbb{R}$}{Real numbers}}; \node[name=complex, below of=real, NobleGas] {\NaturalElementTextFormat{$0$}{local}{$\mathbb{C}$}{Complex numbers}}; \node[name=quat, below of=complex, AlkaliMetal] {\NaturalElementTextFormat{$0$}{\phantom{0}}{$\mathbb{H}$}{Quaternions}}; \node[name=oct, below of=quat, AlkalineEarthMetal] {\NaturalElementTextFormat{$0$}{\phantom{0}}{$\mathbb{O}$}{Octonions}}; \node[name=sed, below of=oct, Halogen] {\NaturalElementTextFormat{$0$}{\phantom{0}}{$\mathbb{S}$}{Sedenions}};

\node[name=CD, below of=sed, Halogen] {\NaturalElementTextFormat{$0$}{\phantom{0}}{$\mathrm{CD}_{\mathbb{R}}(n)$}{\small{Cayley-Dickson construction}}};

%% group a

\node[name=splitquat, left of= quat, Halogen] {\NaturalElementTextFormat{$0$}{\phantom{0}}{$\mathbb{H}^{{\oplus2}$}{\scriptsize{Split-quaternions} }}}; \node[name=realcliff, below of= splitquat, Halogen] {\NaturalElementTextFormat{$0$}{\phantom{0}}{$C \ell_{i,j}(\mathbb{R})$}{\scriptsize{Real $(p,q)$-Clifford algebra }}};

%% group b \node[name=bicomplex, right of= quat, Halogen] {\NaturalElementTextFormat{$0$}{\phantom{0}}{$\mathbb{C}^{{\oplus2}$}{Bicomplex} numbers}}; \node[name=biquat, below of= bicomplex, Halogen] {\NaturalElementTextFormat{$0$}{\phantom{0}}{$C \ell _{2}(\mathbb{C})$}{Biquaternions}}; \node[name=complexcliff, below of= biquat, Halogen] {\NaturalElementTextFormat{$0$}{\phantom{0}}{$C \ell _{n}(\mathbb{C})$}{\scriptsize{Complex $n$-Clifford algebra}}};

%% Group 6 - IVB \node[name=intfinrat, right of= rat, Element] {\NaturalElementTextFormat{$0$}{\phantom{0}}{$\mathcal{O}_{\mathbb{Q}(\mathrm{A})}$}{\small{Ring of integers of $\mathbb{Q}(\mathrm{A})$}}}; \node[name=algintegers, below of= intfinrat, Element] {\NaturalElementTextFormat{$0$}{\phantom{0}}{$\mathbb{A}$}{Algebraic integers}};

%% Group 6 - IVB \node[name=finrat, right of= algintegers, NobleGas] {\NaturalElementTextFormat{$0$}{global}{$\mathbb{Q}(\mathrm{A})$}{\small{Finite, algebraic extension of $\mathbb{Q} $}}}; \node[name=algrat, below of= finrat, NobleGas] {\NaturalElementTextFormat{$0$}{\phantom{0}}{$\overline{\mathbb{Q}}$}{Algebraic closure of $\mathbb{Q} $}};

%% Group 7 - IVB

\node[name=pint,above right=0cm and 0cm of finrat, Element] {\NaturalElementTextFormat{$0$}{\phantom{0}}{$\mathbb{Z}{p}$}{ $p$-adic integers}}; \node[name=pintrat, below of= pint, Element] {\NaturalElementTextFormat{$0$}{\phantom{0}}{$\mathcal{O}{\mathbb{Q}{p}(\mathrm{A})}$}{\small{Ring of integers of $\mathbb{Q}{p}(\mathrm{A}) $}}};

%% Group 8 - IVB

\node[name=prat, right of= pintrat, NobleGas] {\NaturalElementTextFormat{$0$}{local}{$\mathbb{Q}{p}$}{$p$-adic rational numbers}}; \node[name=algprat, below of= prat, NobleGas] {\NaturalElementTextFormat{$0$}{local}{$\mathbb{Q}{p}(\mathrm{A})$}{\small{Finite, algebraic extension of $\mathbb{Q}{p}$}}}; \node[name=algclprat, below of= algprat, NobleGas] {\NaturalElementTextFormat{$0$}{\phantom{0}}{$\overline{\mathbb{Q}}{p}$}{Algebraic closure of $\mathbb{Q}{p}$}}; \node[name=comalgclprat, below of= algclprat, NobleGas] {\NaturalElementTextFormat{$0$}{\phantom{0}}{$\widehat{\overline{\mathbb{Q}}}{p}$}{\scriptsize{Completion of $\overline{\mathbb{Q}}_{p}$}}};

%% Group 9 - IVB

\node[name=dual, right of= algprat, Element] {\NaturalElementTextFormat{$0$}{\phantom{0}}{$\mathbb{R}[\epsilon]/(\epsilon^{{2})$}{\small{Dual} numbers}}};

\node[name=splitcomplex, right of= dual, Element] {\NaturalElementTextFormat{$0$}{\phantom{0}}{$\mathbb{R}^{{\oplus2}$}{Split-complex} numbers}};

%% Group \node[name=Group1, above of=f, GroupLabel] {\large{[1]} }; \node[name=Group2, above of=p1, GroupLabel] {\large{[2]. [1] $\subseteq$ [2]}}; \node[name=Group3, above of=ffp, GroupLabel] {\large{[3]. [2] $\subseteq$ [3]}}; \node[name=Group4, above of=flsp, GroupLabel] {\large{[4]. [3] $\subseteq$ [4] }}; \node[name=Group5, above of=card, GroupLabel] {\large{[5]. [5] $\subseteq $ [9]}}; \node[name=Group6, above of=hypernat, GroupLabel] {\large{[6]. [6] $\subseteq $ [9]}}; \node[name=Group7, above of=proint, GroupLabel] {\large{[7]. [7] $\subseteq $ [9]}}; \node[name=Group9, above of=splitquat, GroupLabel] {\large{[8]. [8] $\subseteq $ [9]}}; \node[name=Group10, above of=nat0, GroupLabel] {\large{[9]} }; \node[name=Group11, above of=intfinrat, GroupLabel] {\large{[10]. [10] $\subseteq $ [9]}}; \node[name=Group12, above of=bicomplex, GroupLabel] {\large{[11]. [11] $\subseteq $ [9]}}; \node[name=Group13, above of=finrat, GroupLabel] {\large{[12]. [12] $\subseteq $ [9]}}; \node[name=Group14, above of=pint, GroupLabel] {\large{[13]. [13] $\subseteq $ [9]}}; \node[name=Group15, above of=prat, GroupLabel] {\large{[14]. [14] $\subseteq $ [9]}}; \node[name=Group16, above of=dual, GroupLabel] {\large{[15]. [15] $\subseteq $ [9]}}; \node[name=Group17, above of=splitcomplex, GroupLabel] {\large{[16]. [16] $\subseteq $ [9] }};

%% Period \node[name=Period1, left of=f, PeriodLabel] {I}; \node[name=Period1, left of=p1, PeriodLabel] {II}; \node[name=Period1, left of=p2, PeriodLabel] {III}; \node[name=Period1, left of=p3, PeriodLabel] {IV}; \node[name=Period1, left of=p4, PeriodLabel] {V}; \node[name=Period1, left of=pn, PeriodLabel] {VI}; \node[name=Period1, left of=pnn, PeriodLabel] {VII}; \node[name=Period1, left of=p5, PeriodLabel] {VIII}; \node[name=Period1, left of=algp, PeriodLabel] {IX}; \node[name=Period1, left of=add1, PeriodLabel] {X};

%comalgclprat %complexcliff

%% Diagram Title \node at (Group1.west -| Group10.north) [name=diagramTitle, TitleLabel] {\underline{PERIODIC SYSTEM OF NUMBERS}};

\draw[black, NobleGasFill] ($(comalgclprat.north -| complexcliff.east) + (1em,-0.0em)$) rectangle +(1em, 1em) node[right, yshift=-1ex]{Field}; \draw[black, ElementFill] ($(comalgclprat.north -| complexcliff.east) + (1em,-1.5em)$) rectangle +(1em, 1em) node[right, yshift=-1ex]{Commutative ring}; \draw[black, MetalFill] ($(comalgclprat.north -| complexcliff.east) + (1em,-3.0em)$) rectangle +(1em, 1em) node[right, yshift=-1ex]{Semiring}; \draw[black, AlkaliMetalFill] ($(comalgclprat.north -| complexcliff.east) + (1em,-4.5em)$) rectangle +(1em, 1em) node[right, yshift=-1ex]{Associative division ring}; \draw[black, AlkalineEarthMetalFill] ($(comalgclprat.north -| complexcliff.east) + (1em,-6.0em)$) rectangle +(1em, 1em) node[right, yshift=-1ex]{Division ring}; \draw[black, HalogenFill] ($(comalgclprat.north -| complexcliff.east) + (1em,-7.5em)$) rectangle +(1em, 1em) node[right, yshift=-1ex]{Real algebra}; \draw[black, NonmetalFill] ($(comalgclprat.north -| complexcliff.east) + (1em,-9.0em)$) rectangle +(1em, 1em) node[right, yshift=-1ex]{$0=1$}; \draw[black, MetalloidFill] ($(comalgclprat.north -| complexcliff.east) + (1em,-10.5em)$) rectangle +(1em, 1em) node[right, yshift=-1ex]{Proper class};

\node at ($(comalgclprat.north -| complexcliff.east) + (5em,-15em)$) [name=elementLegend, Element, fill=white]{\NaturalElementTextFormat{char}{\tiny{property (of field)}}{Symbol}{Name}};

\node at ($(comalgclprat.north -| complexcliff.east) + (5em,-20em)$) [name=extra1]{$n,i,j \in \mathbb{N}_{0}$,};

\node at ($(comalgclprat.north -| complexcliff.east) + (5em,-21em)$) [name=extra2]{$p$ prime};

\end{tikzpicture} \end{preview} \end{document}