Abstract
Let ℑ be a Gabriel topology on the ring A. In this chapter we will investigate how various finiteness properties of the quotient category Mod-(A, ℑ) are reflected by properties of the ring A. The lattice of subobjects of Mℑ in the category Mod-(A, ℑ) is isomorphic to the lattice Satℑ(M) of ℑ-saturated submodules of M, and the finiteness properties may therefore be formulated for the lattices of ℑ-saturated submodules.
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© 1975 Springer-Verlag Berlin Heidelberg
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Stenström, B. (1975). Finiteness Conditions on Mod-(A, ℑ). In: Rings of Quotients. Die Grundlehren der mathematischen Wissenschaften, vol 217. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-66066-5_15
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DOI: https://doi.org/10.1007/978-3-642-66066-5_15
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-66068-9
Online ISBN: 978-3-642-66066-5
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