If and only if every finitely generated torsion-free R-module is w-projective.
当且仅当每个有限生成无挠R-模是w-投射模。
This paper gives the definition of triangular matrix rings of order 3 Γ, and by establishing an equivalent functor F, proved here is also the equivalence between finitely generated module category mod Γ over triangular matrix algebra Γ of order 3 and category Γ ￡.
文章给出了三级三角矩阵环Г的定义，通过建立一个等价函子F，证明了三角矩阵代数Г上的有限生成模范畴modГ与Г￡是等价的范畴。
If M is a finitely generated module over a regular local ring R. It is well known that the sum of projective dimension and the codimension of M is equal to the global dimension of R.
如果M是正则局部环R上一个有限生成的模，则M的投射维数与余维数的和等于R的整体维数。
Is generalized essential finitely generated - module if and only if for any generalized essential finitely generated sub-module, there exists a type direct summand of such that N ≤ geK.
M是广义基本有限生成的TS1-模当且仅当对M的任意广义基本有限生成子模N，存在KtM，使得N≤geK。
Let г be 3 order triangular matrix algebra, mod Γ be finitely generated module category over Γ and Γ~ζ equivalent category with Γ.
设Γ是三级三角矩阵代数，modΓ表示Γ上的有限生成模范畴，Γζ是与modΓ等价的范畴。
Finitely generated graded R-module
有限生成分次R－模
Let R be a Dedekind domain and M a finitely generated torsion R module, then End (R) is semi perfect.
设R为Dedekind整环，M是有限生成的扭R模，那么End（RM）为半完全环。