projective dimension meaning in English
射影维数
Examples
- 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，我们定义了平坦模的投射维数，用它刻划了一些环，并讨论了cotorsion模和严坦模的投射维数的关系。 - 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为无平方强稳定理想时i ~ c = i ，因而i ~ c和i的分次betti数、投射维数和正则度相同，本文主要研究i为无平方稳定理想时， i ~ c和i之间分次betti数的关系。 - 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
在第二章中我们将通过另一种方法，也就是考察所有的短正合列以及短正合列之间的态射，我们得到一个新的范畴，通过对这个范畴(我们称之为短正合列范畴c _ rm )的一些基本性质的考察，我们定义出与环r相关的同调维数，我们称它为正合投射维数。 - 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
在第三节中证明了当i为无平方稳定理想时， shiftij ( i )与i的分次betti数、投射维数和正则度相同，从而i ~ c与i的分次betti数、投射维数和正则度相同，最后将所得结论推广到单纯复形上。