Prime Ideals and Decompositions of Modules

  • Roger Wiegand
  • Sylvia Wiegand
Part of the Mathematics and Its Applications book series (MAIA, volume 520)


During thirty years of fascination with prime ideals and decompositions of finitely generated modules over commutative rings, the authors have observed an intriguing interplay between the two topics: these connections are apparent in a wide range of results for both Noetherian and non-Noetherian rings. The Noetherian property itself exemplifies a connection: module decompositions generally work better for Noetherian rings than for non-Noetherian ones, and the prime ideal behavior also seems better (somewhat— see section 2!). Similarly, certain other properties of rings (such as being a valuation ring or being Henselian) simultaneously affect how the modules decompose and how the prime ideals fit together.


Prime Ideal Local Ring Maximal Ideal Commutative Ring Valuation Ring 
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Copyright information

© Springer Science+Business Media Dordrecht 2000

Authors and Affiliations

  • Roger Wiegand
    • 1
  • Sylvia Wiegand
    • 1
  1. 1.Department of Mathematics and StatisticsUniversity of NebraskaLincolnUSA

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