injective 中文意思是什麼

Then we investigate the minquasi - injective modules with some additional conditions. finally, we study the endomorphism ring on minquasi - injecive modules

其次，我們研究了帶有附加條件的min - q -內射模的性質。

Injective envelops and generators in the entwined module categories

扭曲模的內射包和生成子

Injective modules play an important role in module theory and homological algebra. in the first part of this paper, the concept of injective modules extended and weak injective modules are denned

在本文的第一部分中，我們對內射模的定義進行了推廣，定義了弱內射模：設t ， n為r -模，對于n的任意非零子模m （

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 ( rr ) = soc ( rr ) and r contains an injective maximal left ideal

第一章主要將「 duo -環」條件替換成「每一極大左（右）理想是gw -理想」條件，研究在此條件下， gp - v -環的強正則性，證明了： （ 1 ） r是強正則環當且僅當r是左gp - v -環且r的每一極大左理想是廣義弱理想； （ 2 ） r是強正則環當且僅當r是左gp - v -環且r的每一極大右理想是廣義弱理想，第二章，主要將gp - v -環上一些結果推廣到gp - v -環上，討論gp - v -環的正則性，證明了： （ 1 ） r是左自內射正則環且soc （ _ rr ） 0當且僅當r是包含內射極大左理想的gp - v -環，且soc （ _ rr ） = soc （ r _ r ） ； （ 2 ） r是正則環且每一極大本質左理想是理想當且僅當r是左gp -內射的左gp - v -環且每一極大本質左理想是理想。

E. e. enochs put forword the concepts of injective ( projective or flat ) ( pre ) cover and ( pre ) envelope in the early 1980s ", a lot of articles have studied existence and uniqueness of such ( pre ) covers and ( pre ) envelopes, the property of their kernels or cokernels, and character many special rings. moreover, if such kind of ( pre ) covers or ( pre ) envelopes exist, we can construct a complete injective ( projective or flat ) resolvent ( called resolution when exact ) and a partial injective ( projective or flat ) resolvent, and if r is a ring, we can study the relationship of its left global dimension l. d ( r ) ( or its weak dimension w ( r ) ) and the properties of syzygies ( or cosyzygies ) of a resolvent ( or resolution ), and the relationship of its left global dimension l. d ( r ) ( or its weak dimension ) and the exactness of a resolvent ( or resolution )

自八十年代初e . e . enochs首次提出並研究內射（投射、平坦） （預）蓋及內射（投射、平坦） （預）包這些概念以來，大批論文研究此類包、蓋的存在性、唯一性問題以及它們的核、上核的性質，並據此刻畫了一些常見的特殊環；更進一步地，當此類包、蓋存在時，我們可構造相應的完全投射（平坦、內射）預解式（當正合時稱為完全分解式）以及單邊投射（平坦、內射）預解式，研究了環的左（右）總體維數、弱維數與此類分解式的合沖模（或上合沖模）的性質、復形正合性之間的關系。

At first a lot of new characterizations of gorenstein injective modules are given, then the author claim that a ring r is qf if and only if every left ( or right ) r - modules are gorenstein injective, and then show that if r is two - side noetherian, r is n - gorenstein if and only if every n - th cosyzygy of an injective resolution of a left ( and right ) r - module is gorenstein injective if and only if every n - th syzygy of an injective resolvent of a left ( and right ) right module is gorenstein injective. finally, we prove that for an n - gorenstein ring r with n > 0, every module can be embedded in a gorenstein injective module and the injective dimension of its cokernel is at most n - 1

首先給出了gorenstein內射模的許多新的刻畫，推出了環r是qf環當且僅當每個左（右）的r -模的單邊內射分解式的第n個上合沖是gorenstein內射模，接著推出了左、右noether環只是n - gorenstein環當且僅當每個左（右）模的單邊內射分解式的第n個上合沖是gorenstein內射模當且僅當每個左（右）模的單邊內射預解式的第n合沖是gorenstein內射模，最後推出了n - gorenstein環中每個模都可嵌入到一個gorenstein內射模之中，且其上核的內射維數不大於n - 1 。

In the second section, the author studies copure injective modules, which are the kernels of injective precovers. at first the author gives some characterizations of copure injective modules, show many characterizations of reduced copure injective modules, and then study when injective precover is exact. moreover, the author claims that if l. pid ( r ) of a ring is finite, some copure injective modules can be obtained by a resolvent, finally analyze the relationship between syzygies of a resolvent and cosyzygies of a resolution on n - gorenstein rings

第二部分著重研究了上純內射模，即內射預蓋的核，首先給出了上純內射模的一些等價刻畫，然後給出了約化的上純內射模的等價刻畫，接著研究了內射預蓋在什麼條件下正合，再接著研究了當環的l . pid （ r ）有限時由模的內射預（分）解式可得到一些上純內射模，最後討論了n - gorenstein環中單邊內射預解式的合沖模與單邊內射分解式的上合沖模之間的聯系。

On yj - injective modules and characteristic properties of strongly regular rings

內射模與強正則環的刻畫

Using universal property, we can define general ( pre ) cover and ( pre ) envelope, such as gorenstein injective ( projective or flat ) ( pre ) cover and ( pre ) envelope, 5 - torsion free ( pre ) cover etc. in a word, problems on ( pre ) over and ( pre ) envelope have aroused considerable debate in the academic circle, which embodies flexible use of tools of homological algebra in studying categories of rings and modules

而且利用泛性我們又可定義更廣泛意義上的包、蓋問題，例如： gorenstin內射（平坦、投射）包（蓋） ， s -無撓預蓋，等等。用這類比內射（平坦、投射）更廣泛意義上的特殊模又能刻畫一些環。總之，包、蓋問題是當今非常活躍的研究課題，體現了同調代數在環模範疇研究中靈活運用。

In this thesis, we will discuss the homological dimension and homological properities of rings and modules which is one of the most impertinent parts in homological theory. in the first chapter, we investigate the relation of homological properities between ring r. [ [ x ] ] and ring r, we prove that a module m is an injective or a flat r - module, then it is an injective or a flat r [ [ x ] ] - module respectively, and if m is an injective or a flat r - module, then hom ( r [ [ x ] ], m ) is an injective r [ [ x ) ] - module, r. [ [ x } ] m is a flat r { [ x ] } - module

在第一章中，我們主要研究了冪級數環r [ [ x ] ]與環r上的模的平坦性與內射性之間的關系。證明了當只是一個完全凝聚交換環時，如果m是一個內射或平坦r [ x ] -模，則m是一個內射或平坦r -模。如果m是一個平坦r -模，則r [ x ] _ rm是一個平坦r [ x ] -模。

It is bijective if both injective and sujective.

既單又滿的映射稱為一一對應。

On injective lattice implication algebras

關于內射的格蘊涵代數

The injective numerical results showed that the injection of upstream near the rotor leading 30 % axial chord edge can suspend the stall

噴氣數值計算結果表明，轉子上游約30 %軸向弦長處的噴氣推遲了失速的發生。

A characterization of quasi - continuous modules using relatively injective

使用相關內射性對擬連續模的一個刻劃

In chapter 2, we discuss several properties of relative injective modules over a formal triangular matrix rings

第二部分討論了形式三角矩陣環上的幾種相對內射模的性質。

Meanwhile, we describe injectivity conditions over a formal triangular matrix rings in views of the studies for essential, nearly, f, n - generated and weakly relative injective modules

通過對基本、 nearly 、 f 、 n -生成和弱相對內射模的研究，進一步討論了形式三角矩陣環上的內射模。

Equivalent conditions and properties on ep - injective rings

內射環的等價刻畫及性質

In the second part of this paper, using of linear compact and injective cogenerator so on, we discuss the relations between morita duality and weak morita duality. in [ 16 ], n - absolutely pure modules, n - flat modules and n - coherent rings are defined

在文獻[ 16 ]中，作者定義了n -絕對純模和n -平坦模，並在此意義下將凝聚環推廣碩士學位論文:弱內射模與弱morit 。

Weak injective module and weak injective dimension

弱內射模與弱內射維數

Generalized essentially relative injective modules

廣義基本相對內射模