ON ORDERED MONOID RINGS OVER A QUASI-BAER RING
ON ORDERED MONOID RINGS OVER A QUASI-BAER RING
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DOI：
10.1081/agb-100002171
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发表时间：
2001-04
影响因子：
0.7
通讯作者：
Y. Hirano
中科院分区：
文献类型：
--
作者：
Y. Hirano
如果环R的每一个（主）左理想的左湮灭子是由一个幂等子生成的，则称环R为（左主）拟贝尔。我们证明了如果R是（左主）拟baer， G是一个有序单群，那么单群环RG也是（左主）拟baer。当R是（左主要）拟baer， G是作用于R的有序群时，给出了偏群环r# G是（左主要）拟baer的充分必要条件。
A ring R is called (left principally) quasi-Baer if the left annihilator of every (principal) left ideal of R is generated by an idempotent. We show that if R is (left principally) quasi-Baer and G is an ordered monoid, then the monoid ring RG is again (left principally) quasi-Baer. When R is (left principally) quasi-Baer and G is an ordered group acting on R, we give a necessary and sufficient condition for the skew group ring R♯G to be (left principally) quasi-Baer.