injective dimension 中文意思是什麼
injective dimension
解釋
單射維數-
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 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。 -
Weak injective module and weak injective dimension
弱內射模與弱內射維數 -
Generalized gorenstein injective modules and dimension
內射模和維數 -
In chapter 3, we discuss n - flat modules and n - fp - injective modules, we define n - flat dimension and n - fp - injective dimension, we consider n - flat modules and n - fp - injective modules in commutative n - coherent rings, their properties are similar to flat and injectivc modules in commutative coherent rings
在第三章中，我們主要討論了n -平坦模和n - fp內射模，定義了n -平坦維數和n - fp內射維數，並考慮了交換n -凝聚環中的n -平坦模和n - fp內射模。他們有類似於交換凝聚環中的平坦模和內射模的性質。
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