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Modules of generalized fractions

Part of: Ring extensions and related topics

Published online by Cambridge University Press:  26 February 2010

R. Y. Sharp  and
H. Zakeri
R. Y. Sharp
Affiliation:
Department of Pure Mathematics, The University, Sheffield. S3 7RH
H. Zakeri
Affiliation:
Department of Pure Mathematics, The University, Sheffield. S3 7RH
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Extract

The construction, for a module M over a commutative ring A (with identity) and a multiplicatively closed subset S of A, of the module of fractions S-1M is, of course, one of the most basic ideas in commutative algebra. The purpose of this note is to present a generalization which constructs, for a positive integer n and what is called a triangular subset U of An = A × A × … × A (n factors), a module U-n M of generalized fractions, a typical element of which has the form

where m∈ M and (u1, … un)∈U.

MSC classification

Secondary: 13B30: Rings of fractions and localization
Type
Research Article
Information
Mathematika , Volume 29 , Issue 1 , June 1982 , pp. 32 - 41
Copyright
Copyright © University College London 1982

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