(untitled) (JOURNAL OF ADVANCES IN MATHEMATICS, 2015)
The aim of this work is to study the incidence functions and the tensor product of two incidence algebras. We show that the tensor product of two incidence algebras is an incidence algebra. We believe that our result is true for uncountable locally partial order sets. We present some examples of incidence functions. We study the Jacobson radical of the tensor product of the incidence algebras as well as when a tensor incidence algebra is an algebraic algebra over a field.