Noncommutative $p$-Tachyon

Following a brief review of the tachyon field of $p$-adic string theory, we consider a noncommutative deformation of this field theory. This is done by replacing ordinary products with noncommutative products in the exact effective action of this field. Solitonic lumps corresponding to D-branes are obtained for all values of the noncommutativity parameter $\theta$.