Malcev-Neumann环的主拟Baer性质

摘要

设R是环,G是偏序群,σ是从G到R的自同构群的映射.本文研究了Malcev-Neumann环R*((G))是主拟Baer环的条件.证明了如下结果:如果R是约化环并且σ是弱刚性的,则R*((G))是主拟Baer环当且仅当R是主拟Baer环,并且I(R)的任意G-可标子集在I(R)中具有广义并.%Let R be a ring, G an ordered group and σ a map from G into the group of automorphisms of R. The conditions under which the Malcev-Neumann ring R*((G)) is a principal quasi-Baer ring are investigated in this paper. It is shown that if R is reduced and σ is weakly rigid, then R*((G)) is right p.q.Baer if and only if R is right p.q.Baer and any G-indexed subset of I(R) has a generalized join in I(R).