Abstract
In Commutative Algebra, localization at a prime ideal in a polynomial ring is a basic but important tool. It is well-known that localization at a prime ideal can be computed through “primary decomposition”, however, it contains unnecessary primary components for the localization. In this paper, we propose a method for computing the localization without producing unnecessary primary components. Also, we discuss computation for desirable primary components from a view of “the degree of nilpotency”. In a computational experiment, we see the effectiveness of our method by its speciality.
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Acknowledgements
The author appreciates the kind support of the computational facility by Professor Masayuki Noro. He is grateful to Professor Ernst W. Mayr for his helpful comments during the CASC 2021 conference. He would like to thank Professor Kazuhiro Yokoyama for constructive comments and suggestions for the paper.
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Ishihara, Y. Efficient Localization at a Prime Ideal Without Producing Unnecessary Primary Components. Math.Comput.Sci. 16, 14 (2022). https://doi.org/10.1007/s11786-022-00537-4
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DOI: https://doi.org/10.1007/s11786-022-00537-4