projective dimension 中文意思是什麼

projective dimension 解釋
射影維數
  • projective : adj. 1. 投影的，射影的。2. 凸出的，突出的。3. 【心理學】投射的。
  • dimension : n 1 尺寸。2 【數學】次元，度（數），維（數）。3 【物理學】因次，量網。4 〈pl 〉容積；面積；大小，...
  1. Necessary and sufficient condition of 2 - dimension projective transformation being involution

    二維射影變換是對合的充要條件
  2. 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。
  3. 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，我們定義了平坦模的投射維數，用它刻劃了一些環，並討論了cotorsion模和嚴坦模的投射維數的關系。
  4. When i s is a squarefree strongly stable ideal, ic = i. therefore p and / have the same graded betti numbers, projective dimension and regularity. in this paper, we study the relationship of the betti numbers between ic and i. in section 1, the concepts of combinatorial shifting and some related results are given

    ） s為無平方強穩定理想時i ~ c = i ，因而i ~ c和i的分次betti數、投射維數和正則度相同，本文主要研究i為無平方穩定理想時， i ~ c和i之間分次betti數的關系。
  5. In the second chapter, we attain this goal by another route. collecting all short exact sequence and the morphisms among them, we get a new category, call the short exact sequences category crm. we define a global dimension attached to the original ring r from the view of the short exact sequences category cr. m, named the exact projective dimension

    在第二章中我們將通過另一種方法，也就是考察所有的短正合列以及短正合列之間的態射，我們得到一個新的范疇，通過對這個范疇（我們稱之為短正合列范疇c _ rm ）的一些基本性質的考察，我們定義出與環r相關的同調維數，我們稱它為正合投射維數。
  6. In section 3, we show that when i is a squarefree stable ideal, shiftij ( i ) and i have the same graded betti numbers, projective dimension and regularity, then ic and i have the same graded betti numbers, projective dimension and regularity. at last we apply the results we obtained to simplicial complexes

    在第三節中證明了當i為無平方穩定理想時， shiftij （ i ）與i的分次betti數、投射維數和正則度相同，從而i ~ c與i的分次betti數、投射維數和正則度相同，最後將所得結論推廣到單純復形上。
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