Honam Mathematical Journal (호남수학학술지)

The Honam Mathematical Society (호남수학회)
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A FORMAL DERIVATION ON INTEGRAL GROUP RINGS FOR CYCLIC GROUPS

  • Joongul Lee (Department of Mathematics Education, Hongik University)
  • Received : 2023.04.11
  • Accepted : 2023.05.28
  • Published : 2023.12.20
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Abstract

Let G be a cyclic group of prime power order pk, and let I be the augmentation ideal of the integral group ring ℤ[G]. We define a derivation on ℤ/pkℤ[G], and show that for 2 ≤ n ≤ p, an element α ∈ I is in In if and only if the i-th derivative of the image of α in ℤ/pkℤ[G] vanishes for 1 ≤ i ≤ (n - 1).

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Acknowledgement

This work was supported by 2019 Hongik University Research Fund.

References

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  2. L. C. Washington, Introduction to Cyclotomic Fields, Graduate Texts in Mathematics, VOl. 83, Second Edition, Springer-Verlag, New York, 1997.