Product of generalized $p-$K\"ahler manifolds

A product of K"ahler manifolds also carries a K"ahler metric. In this short note we would like to study the product of generalized $p-$K"ahler manifolds, compact or not. The results we get extend the known results (balanced, SKT, sG manifolds), and are optimal in the compact case. Hence we can give new non-trivial examples of generalized $p-$K"ahler manifolds.