Digital (co)homology modules and digital Pontryagin algebras

In the current study, we explore digital homology and cohomology modules, and investigate their fundamental properties on pointed digital images. We also examine pointed digital Hopf spaces and base point preserving digital Hopf functions between the pointed digital Hopf spaces with suitable digital multiplications, and explore the digital primitive homology and cohomology classes, the digital Pontryagin algebras and coalgebras on the digital Hopf spaces as digital images.