In this paper, we define a new kind of formal power series rings by using Gaussian binomial coefficients and investigate some properties. More precisely, we call such a ring a Gaussian series ring and study McCoy’s theorem, Hermite properties and Noetherian properties.

Keywords: Gaussian series ring, $q$-torsion-free, McCoy's theorem, right K-Hermite ring, L-Hermite ring, Noetherian ring