injective envelope 中文意思是什麼
injective envelope
解釋
內射包絡, 單射包絡-
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。 -
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。
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