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Ideal Transforms with Respect to a Pair of Ideals

Abstract

We introduce the ideal transform functor D I,J with respect to a pair of ideals (I,J) which is an extension of the ideal transform functor D I of Brodmann. Some equivalent conditions on the exactness of the ideal transform functor will be shown in the paper. We also study the finiteness of the sets Ass R (R i D I (N)) and Ass R (R i D I, J (M,N)).

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References

  1. 1.

    Bahmanpour, K.: Exactness of ideal transforms and annihilators of top local cohomology modules. J. Korean Math. Soc. 52(6), 1253–1270 (2015)

    MathSciNet  Article  MATH  Google Scholar 

  2. 2.

    Brodmann, M.P., Sharp, R.Y.: Local Cohomology: An algebraic introduction with geometric applications, 2nd edn. Cambridge University Press, Cambridge (2013)

    Google Scholar 

  3. 3.

    Divaani-Aazar, K., Sazeedeh, R.: Cofiniteness of generalized local cohomology modules. Colloq. Math. 99(2), 283–290 (2004)

    MathSciNet  Article  MATH  Google Scholar 

  4. 4.

    Nam, T.T., Tri, N.M.: Generalized ideal transforms. Stud. Sci. Math. Hung. 51(1), 67–82 (2014)

    MathSciNet  MATH  Google Scholar 

  5. 5.

    Nam, T.T., Tri, N.M., Dong, N.V.: Some properties of generalized local cohomology modules with respect to a pair of ideals. Int. J. Algebra Comput. 24(7), 1043–1054 (2014)

    MathSciNet  Article  MATH  Google Scholar 

  6. 6.

    Rotman, J.: An introduction to homological algebra. Academic, New York (2009)

    Book  MATH  Google Scholar 

  7. 7.

    Takahashi, R., Yoshino, Y., Yoshizawa, T.: Local cohomology based on a nonclosed support defined by a pair of ideals. J. Pure Appl. Algebra 213, 582–600 (2009)

    MathSciNet  Article  MATH  Google Scholar 

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Acknowledgements

This research is funded by Vietnam National Foundation for Science and Technology Development (NAFOSTED) under Grant No. 101.04-2015.22.

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Correspondence to Tran Tuan Nam.

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Tri, N.M., Nam, T.T. Ideal Transforms with Respect to a Pair of Ideals. Acta Math Vietnam 42, 701–715 (2017). https://doi.org/10.1007/s40306-017-0213-4

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Keywords

  • Local cohomology
  • Ideal transforms
  • Associated primes

Mathematics Subject Classification (2010)

  • 13D45