Abstract
When A is a right non-singular ring, its maximal right ring of quotients Qmax is obtained as A E , where E is the family of all essential right ideals of A, and Mod-(A, E) consists of the non-singular injective A-modules. It follows from Prop. X.1.7 that every object in the category Mod-(A, E) is injective. Thus Mod-(A, E) is a spectral category. In view of this observation, it is natural to begin this chapter with a study of the properties of spectral categories in terms of a standard representation as a Giraud subcategory of a module category.
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© 1975 Springer-Verlag Berlin Heidelberg
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Stenström, B. (1975). The Maximal Ring of Quotients of a Non-Singular Ring. In: Rings of Quotients. Die Grundlehren der mathematischen Wissenschaften, vol 217. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-66066-5_14
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DOI: https://doi.org/10.1007/978-3-642-66066-5_14
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-66068-9
Online ISBN: 978-3-642-66066-5
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