On(N,U)-Coherence of Modules and Rings |
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作者姓名: | ZhongKuiLIU JavedAHSAN |
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作者单位: | [1]DepartmentofMathematics.NorthwestNormalUniversity,Lanzhou730070,P.R.China [2]DepartmentofMathematicalSciences,KingFahdUniversityofPetroleumandMinerals,Dhahran,31261,SaudiArabia |
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摘 要: | Let U be a flat right R-module and N an infinite cardinal number.A left R-module M is said to be (N,U)-coherent if every finitely generated submodule of every finitely generated M-projective module in σ[M] is (N,U)-finitely presented in σ[M].It is proved under some additional conditions that a left R-module M is (N,U)-coherent if and only if Л^Ni∈I U is M-flat as a right R-module if and only if the (N,U)-coherent dimension of M is equal to zero.We also give some characterizations of left (N,U)-coherent dimension of rings and show that the left N-coherent dimension of a ring R is the supremum of (N,U)-coherent dimensions of R for all flat right R-modules U.
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关 键 词: | 模论 环论 (N U)一致性 无限基数 |
收稿时间: | 2000-08-21 |
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