Buchsbaum modules and parameter ideals under flat extensions

Let $(R,\frak m)$ and $(S, \frak n)$ be commutative Noetherian local rings, let $\varphi: R\to S$ be a flat local homomorphism. In this paper, we first characterize the ascent and descent of Buchsbaum modules and generalized Cohen-Macaulay modules via the flat extension $\varphi$. Then, we provide relationships between the parameter ideals of a finitely generated $R$-module $M$ and those of $M\otimes_RS$ under the assumption that $\frak{n} = \frak{m} S.$