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IDEAL CHAINS IN RESIDUALLY FINITE DEDEKIND DOMAINS

Part of: Sequences and sets Algebraic number theory: global fields

Published online by Cambridge University Press:  28 November 2018

YU-JIE WANG Open the ORCID record for YU-JIE WANG [Opens in a new window] ,
YI-JING HU Open the ORCID record for YI-JING HU [Opens in a new window]  and
CHUN-GANG JI Open the ORCID record for CHUN-GANG JI [Opens in a new window]
YU-JIE WANG
Affiliation:
School of Mathematical Sciences, Nanjing Normal University, Nanjing 210023, PR China email [email protected]
YI-JING HU
Affiliation:
School of Mathematical Sciences, Nanjing Normal University, Nanjing 210023, PR China email [email protected]
CHUN-GANG JI*
Affiliation:
School of Mathematical Sciences, Nanjing Normal University, Nanjing 210023, PR China email [email protected]
*
✉[email protected]
Rights & Permissions [Opens in a new window]

Abstract

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Let $\mathfrak{D}$ be a residually finite Dedekind domain and let $\mathfrak{n}$ be a nonzero ideal of $\mathfrak{D}$. We consider counting problems for the ideal chains in $\mathfrak{D}/\mathfrak{n}$. By using the Cauchy–Frobenius–Burnside lemma, we also obtain some further extensions of Menon’s identity.

Keywords

residually finite Dedekind domainMenon’s identitygroup action

MSC classification

Primary: 11R04: Algebraic numbers; rings of algebraic integers
Secondary: 11B13: Additive bases, including sumsets
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 99 , Issue 1 , February 2019 , pp. 56 - 67
Copyright
© 2018 Australian Mathematical Publishing Association Inc. 

Footnotes

This work was partially supported by the Grant No. 11471162 from NNSF of China and the Specialized Research Fund for the Doctoral Program of Higher Education of China (Grant No. 20133207110012).

References

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