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Ideal Transforms with Respect to a Pair of Ideals

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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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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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Authors and Affiliations

  1. Department of Natural Science Education, Dong Nai University, Dong Nai, Vietnam

    Nguyen Minh Tri

  2. Faculty of Mathematics, Computer Science, University of Science, VNU-HCM, Ho Chi Minh City, Vietnam

    Nguyen Minh Tri

  3. Department of Mathematics-Informatics, Ho Chi Minh University of Pedagogy, Ho Chi Minh City, Vietnam

    Tran Tuan Nam

Authors
  1. Nguyen Minh Tri
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  2. Tran Tuan Nam
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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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  • DOI: https://doi.org/10.1007/s40306-017-0213-4

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