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。
Every module is a submodule an injective module and a homomorphic image of a projective module.
任何模都是内射模的子模，也是投射模的同态像。
These conditions are also shown to be necessary and sufficient for an injective module over a cellular algebra to be projective.
讨论了胞腔代数上的投射-内射模，一些关于胞腔代数上的投射模的内射性和内射模的投射性的充分必要条件被给出； 6。
Furthermore, it is shown that every pure projective left R-module is closed under pure submodule if and only if every pure injective left R-module is closed under pure epimorphic image.
最后，作为应用，证明了每一纯投射左R-模在纯子模下封闭当且仅当每一纯内射左R-模在纯满像下封闭。
This Paper gives and proves the dual module of a projective module over aright hereditary and right perfect ring is stil projective.
本文给出并证明了右遗传、右完备环上投射模的对偶模仍然是投射模。
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。
The approach adopted here is largely homological, based upon the cell module filtration of projective modules and the dimension shifting of some exact sequences involving cell modules.
我们的研究主要采用同调的方法，许多论证用到胞腔代数上投射模所具有的滤过性质和一些涉及胞腔模的正合列的维数转移。
When R is left and right Π coherent ring, a sufficient condition which every f. g. reflexive module is projective is given.
当r是左右∏凝聚环时，给出每个f.g.自反模是投射模的一个充分条件。
The definition of I-projective module and I-projective dimension are introduced and characterized.
给出了I-投射模的定义及M是I-投射模的等价条件，讨论了I-投射维数、整体I-投射维数等相关性质。
We prove that the endomorphism ring of semi - ∑ - quasi-projective module P has stable range at most n provided P is weakly n-epi-projective. Consequently, we partially generalize a main result in [3].
本文证明了若半∑准投射模是弱n满投射的，则其自同态环的稳定秩至多为n，从而部分推广了文献[3]的&个主要结果。
This peper introduces the concept of direct-projective covers, and prove that a ring R is left perfect if and only if every left R-module (flat left R-module) has a direct-projective cover;
本文引入直投射覆盖的概念，证明了环R为左完全环当且仅当每一个左R－模（平坦左R－模）具有直投射覆盖；
Result on the derived couples is obtained, then with the limit of spectral sequences the projective dimension of a finitely presented module over a commutative coherent ring (or commutative coherent quasi-local ring) is characterized.
给出一般情形下关于导出偶的一个结果，然后用谱序列的极限项刻划了可换凝聚环（或可换凝聚局部环）上有限表现模的投射维数。
P is obtained. Hence, we inscribe the perfect ring and obtain that the ring R is perfect iff every semisimple module A is R (A) projective cover.
并利用它刻划了完全环，得出了环R为完全环当且仅当任意半单模A有R（A）&投射复盖。
Finally, it discussed the properties of strong module in QF rings, and characterized QF rings by virtue of Gorenstein projective modules.
在QF环上讨论了强模的性质，用Gorenstein投射模刻画了QF环。
In this paper, the semisimple ring, left hereditary ring, left perfect ring, semiperfect ring, quasi perfect ring and semi local rings are characterized with pseudo projective module.
本文运用伪投射模刻划了半单环、左遗传环、完全环、半完全环、拟完全环和半局部环的性质和特征。
A ring R is said to be a FCGP-ring if each FCG-projective R-module is projective, some equivalent conditions of FCG-projective modules are given, left V-rings and semisimple rings are characterized by FCG-projective modules, characters and equivalent conditions of FCGP-rings are discussed.
环R称为FCGP环，如果任一FCG投射R模都为投射模.给出了FCG投射模的等价条件，并用FCG投射模刻画了左V环和半单环。
We prove that the endomorphism ring of semi - ∑ - quasi-projective module P has stable range at most n provided P is weakly n-epi-projective. Consequently, we partially generalize a main result in [ 3 ].
本文证明了若半∑准投射模是弱n满投射的，则其自同态环的稳定秩至多为n，从而部分推广了文献[3]的&个主要结果。