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Secondary representations for injective modules over commutative Noetherian rings

Published online by Cambridge University Press:  20 January 2009

Rodney Y. Sharp
Rodney Y. Sharp
Affiliation:
Department of Pure Mathematics, University of Sheffield, Sheffield S3 7RH
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There have been several recent accounts of a theory dual to the well-known theory of primary decomposition for modules over a (non-trivial) commutative ring A with identity: see (4), (2) and (9). Here we shall follow Macdonald's terminology from (4) and refer to this dual theory as “ secondary representation theory ”. A secondary representation for an A-module M is an expression for M as a finite sum of secondary submodules; just as the zero submodule of a Noetherian A-module X has a primary decomposition in X, it turns out, as one would expect, that every Artinian A-module has a secondary representation.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 20 , Issue 2 , September 1976 , pp. 143 - 151
Copyright
Copyright © Edinburgh Mathematical Society 1976

References

REFERENCES

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