projective adj. 1.投影的,射影的。 2.凸出的,突出的。 3.【心理学】投射的。 the projective power of the mind 想像力。
dimension n. 1.尺寸。 2.【数学】次元,度(数),维(数)。 3.【物理学】因次,量网。 4.〔pl.〕容积;面积;大小,规模,范围。 5.〔pl.〕〔口语〕女性的胸腰臀尺寸。 of great [vast] dimensions 非常大的;极重大的。 of one dimension 线性的,一维的。 of three dimensions 立体的,三维的。 of two dimensions 平面的,二维的。 scheme [calamity] of vast dimensions 宏大的计划[范围广阔的灾害]。 The girl's dimensions were 38-24-36. 女孩的标准胸腰臀尺寸是38-24-36英寸。 adj. (石料、木材)切成特定尺寸的。 dimension lumber [stone] 切成特定尺寸的木材[石料]。 vt. 1.使形成所需的尺寸。 2.在…上标出尺寸。
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。