Titlebook: Rings of Quotients; An Introduction to M Bo Stenstr?m Book 1975 Springer-Verlag Berlin Heidelberg 1975 Adjoint functor.Coproduct.Prime.Quot

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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

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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

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,Finiteness Conditions on ,-(,, ?), reflected by properties of the ring .. The lattice of subobjects of . in the category .-(., ?) is isomorphic to the lattice Sat.(.) of ?-saturated submodules of ., and the finiteness properties may therefore be formulated for the lattices of ?-saturated submodules.

countenance

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.

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Bombast

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華而不實(shí)

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.

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Juvenile

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 [2], Maranda [1]):