  In this paper, we are concerned with the S-polyregularity the regular dot
product of slice regular functions. We prove that the product of a slice
regular function and right quaternionic polynomial function is a S-polyregular
function and we determinate its exact order. The general case of the product of
any two slice regular functions is also discussed. In fact, we provide
sufficient and necessary conditions to the product of slice regular functions
be a S-polyregular function. The obtained results are then extended to the
product of S-polyregular functions and remain valid for a special dot product.
As consequences we obtain linearization theorems for such S-polyregular
products with respect to the slice regular functions.
