Zip模的扩张(英文)

Extensions of Zip Modules

本文主要证明了:(1)如果右R-模MR是(α,δ)-compatible且(α,δ)-Armendariz,则右R[x;α,δ]-模M[x]是zip模当且仅当右R-模MR是zip模;(2)如果(S,<)是可消无挠严格序幺半群且M_R是S-Armendariz模,则右[[R^S,<]]-模[[M^S,<]]_([[R^S,<]]是zip模当且仅当右R-模M_R是zip模;(3)如果M_R是reduced且σ-compatible模,G为序群,则Malcev-Neumann环R*((G))上模M*((G))_(R*((G)))是zip模当且仅当右R-模M_R是zip模;因此一些文献中关于zip环与zip模的部分结论可以看作是本论文相关结论的推论.

Let Mr be a right.R-module.In this note,we show that:(1) If Mr is an(α,δ)-compatible and(α,δ)-Armendariz module,then M[x]is a zip right R[x;α,δ]-module if and only if Mr is a zip right R-module.(2) If(S,<) is a cancellative torsion-free strictly ordered monoid,and M_r is an S-Armendariz module,then[[M^(S,<)]]_[[RS,<]]is a zip right[[R^(S,<)]]-module if and only if Mr is a zip right R-module.(3) If M_r is a reduced σ-compatible right R-module,and G is an ordered group,then the Malcev-Neumann module M *((G))_(R*((G))) is a zip right R*((G))-module if and only if Mr is a zip right R-module.Consequently,several known results relating to zip rings and zip modules can be obtained as corollaries of our results.