Strongly Flat Modules over Matlis Domains
Strongly Flat Modules over Matlis Domains
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DOI：
10.1080/00927872.2013.851203
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发表时间：
2015-01
影响因子：
0.7
通讯作者：
Sang Bum Lee
中科院分区：
文献类型：
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作者：
Sang Bum Lee
强平坦模是由Bazzoni-Salce [3]引入的，并用来刻画几乎完美域。在这里，我们希望研究强平坦模，更一般地说，在Matlis域上;这些是整环R，使得域Q的射影维数为1。在第二节中，证明了强平坦性的判别准则。我们还证明了在任意整环上，投射模的强平坦子模是投射的（定理3.2），特别地，强平坦理想是投射的（推论3.4），并利用这些结果证明了强平坦维数（这在Matlis整环上是有意义的）与投射维数在> 1时是一致的.
Strongly flat modules were introduced by Bazzoni–Salce [3] and used to characterize almost perfect domains. Here we wish to study strongly flat modules, more generally, over Matlis domains; these are integral domains R such that the field of quotients Q has projective dimension 1. In Section 2, criteria are proved for strong flatness. We also prove that over arbitrary domains, strongly flat submodules of projective modules are projective (Theorem 3.2), in particular, strongly flat ideals are projective (Corollary 3.4) and use these results to show that the strongly flat dimension (which makes sense over Matlis domains) coincides with the projective dimension whenever it is > 1.