Korean J. Math. Vol. 30 No. 2 (2022) pp.187-198
DOI: https://doi.org/10.11568/kjm.2022.30.2.187

On ζ-factors and computing structures in cyclic $n-$roots

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Published: Jun 30, 2022
Keywords:
General number theory, Gr\"{o}bner basis, cyclic $n-$roots
Mathematics Subject Classification:
11A41, 11Z05, 14Q15, 68W30, 14G99

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Rostam Sabeti
Great Lakes Association for Algebra and Computation (GLAAC), A Formation for Elite college students in the State of Michigan, 4258 Graystone Dr., Okemos, MI 48864, U.S.A

Abstract

In this paper, we introduce a new concept in number theory called ζ-factors associated with a positive integer $n$. Applications of ζ-factors are in the arrangement of the defining polynomials in cyclic $n-$roots algebraic system and are thoroughly investigated. More precisely, ζ-factors arise in the proofs of vanishing theorems in regard to associated prime factors of the system. Exact computations through concrete examples of positive dimensions for $n=16,18$ support the results.



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Great Lakes Association for Algebra and Computation

References

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