Abstract
We now return to the development of general tools to be used in the study of rings of quotients. The theory of modular lattices is one such tool, dealing with the abstract aspects of the relation of inclusion between submodules of a module. In the context of rings of quotients, this theory will be indispensable when we shall elucidate the connection between submodules of a given module M and the sub-modules of a module of quotients of M. It may also be remarked that one of the immediate examples of a ring of quotients, not obtainable as a ring of fractions in the sense of Chap. II, is furnished by the completion of boolean algebras, which is a lattice theoretical phenomenon.
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© 1975 Springer-Verlag Berlin Heidelberg
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Stenström, B. (1975). Modular Lattices. In: Rings of Quotients. Die Grundlehren der mathematischen Wissenschaften, vol 217. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-66066-5_5
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DOI: https://doi.org/10.1007/978-3-642-66066-5_5
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-66068-9
Online ISBN: 978-3-642-66066-5
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