hangdog
发表于 2025-3-23 11:39:07
Perfect Localizations, §1), which in many important cases actually is a natural equivalence (e.g. for rings of fractions). In these cases, . must be an exact functor and thus . is flat as a left .-module. But there are several other nice properties of rings of fractions which also extend to these cases. One such property
高度表
发表于 2025-3-23 17:02:17
The Maximal Ring of Quotients of a Non-Singular Ring, and .-(., .) consists of the non-singular injective .-modules. It follows from Prop. X.1.7 that every object in the category .-(., .) is injective. Thus .-(., .) is a spectral category. In view of this observation, it is natural to begin this chapter with a study of the properties of spectral categ
immunity
发表于 2025-3-23 18:53:19
,Finiteness Conditions on ,-(,, ℑ), reflected by properties of the ring .. The lattice of subobjects of . in the category .-(., ℑ) is isomorphic to the lattice Sat.(.) of ℑ-saturated submodules of ., and the finiteness properties may therefore be formulated for the lattices of ℑ-saturated submodules.
countenance
发表于 2025-3-24 00:59:01
Self-Injective Rings,ase when the maximal ring of quotients is a self-injective ring, a case which will be studied in this Chapter. For this we need to examine the properties of self-injective rings in some detail, and we devote the first three sections to that purpose.
星星
发表于 2025-3-24 05:00:31
http://reply.papertrans.cn/84/8305/830424/830424_15.png
Bombast
发表于 2025-3-24 07:57:07
http://reply.papertrans.cn/84/8305/830424/830424_16.png
太空
发表于 2025-3-24 11:49:23
http://reply.papertrans.cn/84/8305/830424/830424_17.png
华而不实
发表于 2025-3-24 17:41:02
Simple Torsion Theories,dempotents. This chapter is devoted to the development of these methods and to their applications to torsion theory, as well as to an account of the basic theory of rings with various minimum conditions.
污点
发表于 2025-3-24 21:02:11
http://reply.papertrans.cn/84/8305/830424/830424_19.png
Juvenile
发表于 2025-3-25 00:23:29
Torsion Theory,en to each torsion theory we associate a ring of quotients. This chapter is devoted to a comprehensive study of the general aspects of torsion. The basic result will be that the particular notion of torsion, used in the theory of rings of quotients, can be desribed in three equivalent ways (Gabriel , Maranda ):