Perspectivity and cancellation in regular rings
Perspectivity and cancellation in regular rings
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DOI：
10.1016/0021-8693(77)90289-7
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发表时间：
1977-09
影响因子：
0.9
通讯作者：
D. Handelman
中科院分区：
文献类型：
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作者：
D. Handelman
这是一种消除律，例如，对于“有限”自内射正则环上的n-生成投射模。事实证明，对于正则环上的n-生成投射模，当环是单位正则时，这个消去律恰好成立（定义如下）。一个相关的问题是L（R）上透视性的传递性。我们证明了R上的2 × 2矩阵环的传递性成立当且仅当R是单位正则的。Bergman的一个例子表明，L（R）本身的传递性是不充分的单位正则性。沿着这条路，我们得到了任意补格的以下结果：
This is a type of cancellation law that works eg, for finitely generated projective modules over a “finite” self-injective regular ring. It turns out that for finitely generated projective modules over regular rings this cancellation law holds precisely when the ring is unit regular [definitions follow). A related problem is the transitivity of perspectivity on L (R). We show that transitivity holds on a two by two matrix ring over R if and only if R is unit regular. An example of Bergman’s is included to show that transitivity on L (R) itself is not sufficient for unit regularity. Along the way, we obtain the following result for arbitrary complemented lattices: