Schauengurg[2] considered more general case and found necessary and sufficient conditions for the cosmash product coalgebra H Q to be a Hopf algebra with a Hopf subalgebra H and a weak projection !

Schauenburg在文獻(xiàn)[2]中把Radford的研究加以推廣，給出了使余smash積HQ為Hopf代數(shù)好吊色中文字幕精品在线观看，H為HQ的子Hopf代數(shù)亚洲日韩久久久久精品影，且具有弱投射π：HQ→H(即π是左模余代數(shù)同態(tài)，且π|_H=id_H)的等價(jià)條件涩涩视频欧美精品。

Then we introduce the concept of(n,0)-projective dimension for modules and rings.It measures how far away a finitely generated module is from being n-presented,and how far away a ring is from being Noetherian.

然后www.av天堂.cim，我們介紹環(huán)與模的(n，0)-投射維數(shù)免费人妻98，它可以衡量一個(gè)有限生成模與n-表現(xiàn)模的差距国产一级迷奸黄片视频大全，以及衡量一個(gè)環(huán)與Noether環(huán)的差距。

In section one, we study regular cu-rings by use of full elements in rings, and give some equivalent conditions for the endomorphism ring of quasi-projective modules and quasi-injective modules to be a cu-ring.

在第一部分欧美久久久黑人精品久久久极品，我們利用環(huán)中的完全元對(duì)正則cu-環(huán)進(jìn)行刻畫人人摸人人干人人操不卡，并給出了擬投射模和擬內(nèi)射模的自同態(tài)環(huán)是cu-環(huán)的一系列等價(jià)條件。

Finally, sufficient and necessary conditions for endomorphism rings of some special modules to be semi-π-regular are given.

最后天码欧美一区免费精品，我們對(duì)半π正則環(huán)作了一定的研究国产三级国产精品三级在专区，給出了一個(gè)直投射模的自同態(tài)環(huán)是半π正則環(huán)的充要條件。

Due to the inspiration of maximal injective module by professor Wang Ming-yi, in chapter two, we introduce the conception of max-projective modules, discuss its properties, applications: the primitive relations between rings and endomorphism rings, an equivalence that is surrounding strongly V.N. rings.

受汪明義教授引進(jìn)極大內(nèi)射模概念的啟發(fā)国产99久久久国产精品下药，在第二章中我們引進(jìn)了極大投射模的概念超碰人人操人日人人，由此討論了它的一些性質(zhì)及其應(yīng)用：環(huán)與自同態(tài)環(huán)之間的本原性關(guān)系jizzjizzjizz亚洲视频；強(qiáng)正則環(huán)的一個(gè)等價(jià)刻劃；并在環(huán)為交換和非交換的情形下分別應(yīng)用有限表現(xiàn)模的極大投射性得出了SF環(huán)和Von Neumann正則環(huán)的關(guān)系欧美一级特黄大片aaa。

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.

最后玖玖色精品在线，作為應(yīng)用，證明了每一純投射左R-模在純子模下封閉當(dāng)且僅當(dāng)每一純內(nèi)射左R-模在純滿像下封閉两男一女一级A片免费看。

Every module is a submodule an injective module and a homomorphic image of a projective module.

任何模都是內(nèi)射模的子模晚上网站h欧美，也是投射模的同態(tài)像。

The innovation of our thesis lies in:1 We do not require quadratic space to have hyperbolic basis. Moreover, we only require M to be projection module instead of free module;2 Eichler transformation is used instead of the traditional matrix transformation in our proof;3 Not only do we extend the relative results obtained by Bak and Vavilov and the results obtained by Vaserstein and You hong , we also simplify the proof significantly.

我們的創(chuàng)新之處在于： 1 不要求二次型空間具有雙曲基毛片视频免费观看高清在线，甚至不要求M是自由模黄色视频100种在线视频，而僅要求M是投射模； 2 我們?cè)谡撟C中使用的是Eichler變換而不是傳統(tǒng)的矩陣www色小姐； 3 我們的結(jié)果不僅推廣了Bak與Vavilov以及Vaserstein與游宏的相應(yīng)結(jié)果一级做a片久久毛片A片，而且論證也極大地簡(jiǎn)化了。

Then we discuss comodule algebra on the Hopf algebroid. If L is finite generated as a left R-projective module, left L-comodule category is equivalent to the left L〓-module category.

然后討論Hopf代數(shù)胚的余模代數(shù)妓女play妓女视频欧美一区二区，如果L是有限生成的左R-投射模国产一本国产一级，那么左L-余模范疇與左L〓-模范疇是等價(jià)的。

In chapter 4, we define the projective dimension of flat modules, use it to characterize many rings, and the relations between cotorsion modules and the projective dimension of flat modules are also given.

在第四章中亚洲一级性交黄片，我們定義了平坦模的投射維數(shù)网站18禁，用它刻劃了一些環(huán)，并討論了Cotorsion模和嚴(yán)坦模的投射維數(shù)的關(guān)系欧美激情在线第三页。

projective cover：投射覆蓋

投射分解|projective resolution | 投射覆蓋|projective cover | 投射模|projective module

projective module：投射模

投射覆蓋|projective cover | 投射模|projective module | 投射生成元|progenerator

pure projective module：純投射模

純自由模:pure free module | 純投射模:pure projective module | 超純水:Ultra-pure water

relative projective module：相對(duì)投射模

相對(duì)同倫群|relative homotopy group | 相對(duì)投射模|relative projective module | 相對(duì)拓?fù)鋦relative topology

quasi-principally projective module：擬主投射模

投影光刻物鏡:projective lithography objective lenses | 擬主投射模:quasi-principally projective module | 投射星半模:projective star semimodules

pure submodule：純子模

純投射:pure projective | 純子模:pure submodule | 純維數(shù):pure dimension