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Acta Mathematica Vietnamica

, Volume 43, Issue 1, pp 125–136 | Cite as

Assassins and Torsion Functors

  • Fred Rohrer
Article

Abstract

Let R be a ring, let \(\mathfrak {a}\subseteq R\) be an ideal, and let M be an R-module. Let \({\Gamma }_{\mathfrak {a}}\) denote the \(\mathfrak {a}\)-torsion functor. Conditions are given for the (weakly) associated primes of \({\Gamma }_{\mathfrak {a}}(M)\) to be the (weakly) associated primes of M containing \(\mathfrak {a}\), and for the (weakly) associated primes of \(M/{\Gamma }_{\mathfrak {a}}(M)\) to be the (weakly) associated primes of M not containing \(\mathfrak {a}\).

Keywords

Torsion functor Assassin Weak assassin Non-noetherian ring Well-centered torsion theory Weakly proregular ideal 

Mathematics Subject Classification (2010)

Primary 13C12 Secondary 13D30 13D45 

Notes

Acknowledgements

I thank the referee for his careful reading and his suggestions, and – as so often – Pham Hung Quy for suggesting nice counterexamples.

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Copyright information

© Institute of Mathematics, Vietnam Academy of Science and Technology (VAST) and Springer Nature Singapore Pte Ltd. 2017

Authors and Affiliations

  1. 1.BuchsSwitzerland

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