Cellularity of a Larger Class of Diagram Algebras

In this paper, we realize the algebra of $\mathbb{Z}_2$-relations, signed partition algebras and partition algebras as tabular algebras and prove the cellularity of these algebras using the method of \cite{GM1}. Using the results of Graham and Lehrer in \cite{GL}, we give the modular representations of the algebra of $\mathbb{Z}_2$-relations, signed partition algebras and partition algebras.