查询词典 injective envelope

The first chapter, main instead " duo-ring " condition of " every maximal left ideal is GW-ideal " condition,study strongly regularities of GP-V-ring on this condition.lt is shown that (1) R is strongly regular iff R is left GP-V-ring whose maximal left ideals are GW-ideal.(2)R is strongly regular iff R is left GP-V-ring whose maximal right ideals are GW-ideal. The second chapter, generalize some results of GP-V-ring to GP-V-ring, discuss regularity of GP-V-ring.It is shown that (1) R is left self-injective regular with non-zero socle iff R is left GP-V -ring with Soc = Soc and R contains an injective maximal left ideal.(2)R is regular ring and every maximal essential left ideal is ideal iff R is left GP-injective left GP-V -ring and every maximal essential left ideal is ideal.

第一章主要将"duo-环"条件替换成"每一极大左理想是GW-理想"条件，研究在此条件下，GP-V-环的强正则性，证明了：(1)R是强正则环当且仅当R是左GP-V-环且R的每一极大左理想是广义弱理想；(2)R是强正则环当且仅当R是左GP-V-环且R的每一极大右理想是广义弱理想，第二章，主要将GP-V-环上一些结果推广到GP-V′-环上，讨论GP-V′-环的正则性，证明了：(1)R是左自内射正则环且Soc≠0当且仅当R是包含内射极大左理想的GP-V′-环，且Soc=Soc；(2)R是正则环且每一极大本质左理想是理想当且仅当R是左GP-内射的左GP-V′-环且每一极大本质左理想是理想。

Finally, it shows that R is von Neumann regular ring if and only if every right .R-module is right pm-injective if and only if every right principal right ideal of R is right pm-injective if and only if every essential right ideal of R is right pm-injective. Furthermore, some good properties are obtained.

最后，得到R是von Neumann正则环当且仅当每个右R-模是右pm-内射当且仅当R的每个主右理想是右pm-内射当且仅当R的每个本质右理想是右pm-内射，以及其他诸多好的性质。

The ann-injective rings start at the angle of annihilator,at the same time,the CT-injective rings start at the angle of cycle tortionless modules.

在第三章，我们引入了CT -内射维数的概念，从维数的角度来更进一步地认识CT -内射。

Moreover, we define weak principally quasi-injective modules and study Jacobson radical of endomorphism ring of weak principally quasi-injective modules.

另外我们还在主拟内射R-模的基础上定义了弱主拟内射R-模，利用零化子对弱主拟内射模上自同态环的Jacobson根的性质进行了讨论。

A ring R is called right co-semihereditary if every finitely cogenerated factor module of a finitely cogenerated injective right R-module is injective.

如果有限余生成内射右R-模的有限余生成商模是内射的，则R称为右余半遗传的。

So in chapter 2, we use P-flat and P-injective modules to characterize some important rings, like SF-rings, Von Neumann regular rings and Coherent rings, etc. In chapter 3, we introduce the homological dimension of P-flat and P-injective modules.

众所周知，正是由于研究各类模以及它们的同调维数，人们才能对环得到更深层次的性质的描述，所以在第二章中，我们就利用了P-平坦模与P-内射模来刻划几种重要的环，如SF环、Von Neumann正则环、凝聚环等。

Secondly, the equivalence proposition of right pm-injective ring is obtained, and if R is right pm-injective ring, then the Jacobson radical of R coincide with the right singular ideal.

其次，得到右pm-内射环的一个等价命题，并证明若R是右pm-内射环，则R的Jacobson根与R的右奇异理想相等。

In recently years, much progress about injective modules has been obtained, particulary about injective test sets and homological dimensions.

近年来，对内射模的研究已经取得了许多令人鼓舞的进展，特别是内射测试集和同调维数的研究。

On the base of the concept, we give the Schanual Lemma about weak injective modules and discuss the properties of the homomorphisms which can be extended in weak injective modules.

Kerβ的β∈Hom_R，都存在γ∈Hom_R使得β=γα成立，则称T为N-弱内射R-模，且称α为T与M的相伴同态。在此定义的基础上我们给出了弱内射模的Schanuel引理，讨论了弱内射模中能进行开拓的同态的性质。

First,the envelope rectangles set was obtained by equiangular rotation the initial envelope rectangle, and the periphery polygon was constructed by calculating the intersection points between the corresponding edges of the envelope rectangles set.

首先利用等角度旋转方法求得封闭曲线的包络矩形集，利用矩形集对应边的交点得到曲线的外包多边形。

That's what makes this mod unique.

这也正是这个MOD独特。

I now feel furious and want to do something.

现在我觉得非常气愤，想做点什么。