injective resolution 中文意思是什麼

injective resolution 解釋
單射分析
  • injective : 內射, 單射
  • resolution : n 1 決心，果斷；堅定，剛毅。2 （議會等的）決定，決議（案）；【法律】〈罕用語〉判決；（疑問等的）...
  1. 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。
  2. 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 。
  3. 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。
  4. Since the k - gorenstein property of ring r x m is an important aspect in the research field, in the first chapter, we have got an equivalent condition for r m as a k - gorenstein ring by study the injective resolution of ring r m. the dimensions of rings is one of the most important parts in homological theory

    在第一章，我們通過對r （ ? ） m內射分解的考察得到了r （ ? ） m成為k - gorenstein環的一個充分必要條件：維數的研究是同調理論中的核心部分，伴隨同調理論的形成，它便一直成為同調代數中研究的焦點。
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