Buchsbaum modules and parameter ideals under flat extensions

Let $(R,\mathfrak{m})$ and $(S,\mathfrak{n})$ be commutative Noetherian local rings, let $\phi :R\to S$ 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 $\phi$. Then, we provide relationships between the parameter ideals of a finitely generated $R$-module $M$ and those of $M{\otimes }_{R}S$ under the assumption that $\mathfrak{n}=\mathfrak{m}S\mathrm{.}$