Injective Modules over Strong Mori Domains
Injective Modules over Strong Mori Domains
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发表时间：
2008
影响因子：
0.3
通讯作者：
Hwankoo Kim;E. S. Kim;Y. S. Park
中科院分区：
文献类型：
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作者：
Hwankoo Kim;E. S. Kim;Y. S. Park
证明了整环R是强Mori整环当且仅当余半除内射R-模的直和是内射的。我们还证明了：若M是强Mori整环R上的非零余半除扭模，且w-dim（R）=1，则M的半除包络同构于M在P上的直和，其中P遍历R的w-极大理想集.
We show that an integral domain R is a strong Mori domain if and only if any direct sum of co-semi-divisorial injective R-modules is injective. We also show that if M is a nonzero co-semi-divisorial torsion module over a strong Mori domain R with w-dim(R)=1, then the semi-divisorial envelope of M is isomorphic to the direct sum of M localized at P, where P runs over the set of w-maximal ideals of R.