homological dimension 中文意思是什麼
homological dimension
解釋
同憚數- homological : adj. ＝ homologous. homologically ad.
- 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，...
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Given a ring, one always takes the supremum of some homological dimension of specified modules to obtain the corresponding global dimension, and to characterize the ring from outside
對于給定的結合環，人們往往通過對其上的一些模的某一種同調維數取上確界而得到環的相應的整體維數，進而從外部刻畫出環的特徵。 -
At the end of this chapter, we get some results about the dimension and its relationship with global dimension of a ring r. in the third chapter, the homological dimensions about ring r m have be discussed
在這一章的最後，我們研究了環r的整體維數與正合投射維數的關系，得到了這兩類維數是相等的，從而給出了整體維數得一類特徵刻畫。 -
In this thesis, we will discuss the homological dimension and homological properities of rings and modules which is one of the most impertinent parts in homological theory. in the first chapter, we investigate the relation of homological properities between ring r. [ [ x ] ] and ring r, we prove that a module m is an injective or a flat r - module, then it is an injective or a flat r [ [ x ] ] - module respectively, and if m is an injective or a flat r - module, then hom ( r [ [ x ] ], m ) is an injective r [ [ x ) ] - module, r. [ [ x } ] m is a flat r { [ x ] } - module
在第一章中，我們主要研究了冪級數環r [ [ x ] ]與環r上的模的平坦性與內射性之間的關系。證明了當只是一個完全凝聚交換環時，如果m是一個內射或平坦r [ x ] -模，則m是一個內射或平坦r -模。如果m是一個平坦r -模，則r [ x ] _ rm是一個平坦r [ x ] -模。 -
In theorem 3 of this chapter, we prove that homological properities and homological dimensions of residue ring play very important roles. the homological properities and homological dimension of coordinate ring have been studied in the thesis of doctor yang jing - hua. in the second chapter, we generalize the results of coordinate ring to power se - ries residue ring
楊靜化在其博士論文中對坐標環進行了同調刻畫。我們在楊靜化的博士論文基礎上，把坐標環的同調性質和同調維數的相關結論推廣到了冪級數剩餘類環上。
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