本文關(guān)鍵詞：Gorenstein投射覆蓋、預(yù)包絡(luò)與相對(duì)上同調(diào)　出處：《南京大學(xué)》2016年博士論文　論文類型：學(xué)位論文

  更多相關(guān)文章： Gorenstein投射模 (預(yù))覆蓋 (預(yù))包絡(luò) 相對(duì)上同調(diào) 廣義Tate上同調(diào) X-Gorenstein投射模

【摘要】：(預(yù))覆蓋和(預(yù))包絡(luò)模類在相對(duì)同調(diào)代數(shù)中發(fā)揮著重要作用。它們可視為內(nèi)射和投射模類的推廣,基于這些不同的模類,我們能夠?qū)θ我饽?gòu)造不同于內(nèi)射和投射的恰當(dāng)分解。通過(guò)證明這些模類的廣泛存在性,在2000年左右,Enochs和Jenda等人給肇始于Eilenberg和Moore的相對(duì)同調(diào)代數(shù)理論奠定了更穩(wěn)固的基礎(chǔ)。應(yīng)用這些恰當(dāng)分解,我們能得出更為一般的維數(shù)、導(dǎo)出函子、(上)同調(diào)模和平衡函子等概念。對(duì)它們的研究豐富拓展了經(jīng)典的同調(diào)理論。全文總共分為四章。第一章敘述了研究背景和主要結(jié)論,并給出了后文中用到的記號(hào)說(shuō)明。第二章探討了Gorenstein投射模何時(shí)成為覆蓋類和預(yù)包絡(luò)類的條件。我們證明了這和經(jīng)典環(huán)論的情形是相似的：若Gorenstein投射模和Gorenstein平坦模等價(jià),則Gorenstein投射模類構(gòu)成一個(gè)覆蓋類。我們還給出了Gorenstein投射模類構(gòu)成一個(gè)預(yù)包絡(luò)類時(shí)環(huán)的完全刻畫。一些特殊條件下的Gorenstein模的覆蓋和包絡(luò)條件也被給出。在第三章中,我們比較了基于不同恰當(dāng)分解的相對(duì)上同調(diào)理論,并給出這些差異消失的一些充分條件,得到了這些條件和廣義Tate上同調(diào)模的關(guān)系。我們證明了,在一定條件下,這兩種上同調(diào)函子的平衡性質(zhì)是等價(jià)的。作為應(yīng)用,我們重新得到了早先的一些已知結(jié)論。最后我們探討了和Auslander類以及Bass類相關(guān)的導(dǎo)出函子。在第四章中,對(duì)于給定的一個(gè)特殊模類X,我們探討了χ-Gorenstein投射模的維數(shù)和覆蓋性質(zhì)。
[Abstract]:(pre) coverage and (pre) envelope modes play an important role in relative homological algebra. They are regarded as generalized injective and projective classes, these different classes of modules based on, we can appropriate decomposition of arbitrary norm structure is different from injective and projective. By proving the existence of these broad class of modules. In 2000, the relative homological algebra Enochs and Jenda et al, Eilenberg and Moore began to lay a more solid foundation. The application of these proper decomposition, we can get a more general dimension, derived functor, (a) modules and balanced functor concept. Their research enriches and develops the theory of classical coherence. This text is divided into four chapters. The first chapter introduces the research background and main conclusions, and gives the mark used. The second chapter discusses the Gorenstein projective modules will be covered and pre envelope of . we show that the classical ring theory situation is similar: if the Gorenstein projective modules and Gorenstein flat modules, projective equivalence, Gorenstein class form a cover class. We give a complete characterization of Gorenstein projective preenvelope class a ring. Gorenstein mode under special conditions of the cover and envelope conditions are also given. In the third chapter, we compare the different appropriate decomposition of relative cohomology based on the theory, some sufficient conditions are given and these differences disappeared, these conditions were obtained and generalized Tate cohomology relations. We prove that, under certain conditions, these two kinds of balance the nature of the homology functor is proved. As applications, we get some known conclusions earlier. At last we discussed and Auslander and Bass related to the derived functor. In the fourth chapter, for As a special class of X, we discuss the dimension and the covering properties of the X -Gorenstein projective modules.

【學(xué)位授予單位】：南京大學(xué)
【學(xué)位級(jí)別】：博士
【學(xué)位授予年份】：2016
【分類號(hào)】：O189.22

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