正则WB-环

On Regular WB-Rings

引进了WB-环，研究了正则环为WB-环的等价刻画．如果A是正则环R上的有限生成投射右模而且Mn（R）都是WB-环（n∈N），若B，C是任何右犀模而且AOB≌AOC，证明了存在正交理想I，J，使得B／BI≤＋C／CI且C／CJ≤＋B／BJ．这也给出了QB-环上新的模比较性质．

We introduce the concept of WB-rings and investigate the necessary and sufficient conditions under which a regular ring is a WB-ring. Let A be a finitely generated projective right module over a regular ring R. Suppose that Mn（R） is a WB-ring for all n ∈ N. If B and C are any right R-modules such that A ＋ B ≌ A ＋ C, we prove that there exist orthogonal ideals I and J such that B/BI ≤＋C/CI and C/CJ ≤＋ B/BJ. This also gives some new comparable properties of modules over QB-rings.