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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Torsion theory and associated primes


Author: Paul-Jean Cahen
Journal: Proc. Amer. Math. Soc. 38 (1973), 471-476
MSC: Primary 13C10
MathSciNet review: 0357384
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Abstract: A torsion theory partitions the spectrum of the base ring into two sets. Over a Noetherian ring, every suitable partition of the spectrum gives rise to one and only one torsion theory. It is possible to know whether a module is torsion or torsion-free by looking at its associated primes. The example of the polynomial torsion theory is developed.


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DOI: https://doi.org/10.1090/S0002-9939-1973-0357384-6
Keywords: Torsion theory, associated primes, support of a module, partition of the spectrum, reduced primary decomposition, module of polynomials
Article copyright: © Copyright 1973 American Mathematical Society