A Series of Inverse of Ideals in Discrete Valuation Domains (DVR)

Dwi Mahanani

Proceedings of the 2nd International Conference on Education, ICE 2019, 27-28 September 2019, Universitas Muhammadiyah Purworejo, Indonesia

Research Article

A Series of Inverse of Ideals in Discrete Valuation Domains (DVR)

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@INPROCEEDINGS{10.4108/eai.28-9-2019.2290999,
    author={Dwi Mifta Mahanani},
    title={A Series of Inverse of Ideals in Discrete Valuation Domains (DVR)},
    proceedings={Proceedings of the 2nd International Conference on Education, ICE 2019, 27-28 September 2019, Universitas Muhammadiyah Purworejo, Indonesia},
    publisher={EAI},
    proceedings_a={ICE},
    year={2020},
    month={2},
    keywords={dual of ideals discrete valuation domains fractional ideals pid simple modules valuation domains},
    doi={10.4108/eai.28-9-2019.2290999}
}

Dwi Mifta Mahanani
Year: 2020
A Series of Inverse of Ideals in Discrete Valuation Domains (DVR)
ICE
EAI
DOI: 10.4108/eai.28-9-2019.2290999

Dwi Mifta Mahanani¹^,*

1: Universitas Brawijaya

*Contact email: mdwimifta@ub.ac.id

Abstract

This article discusses some properties related to fractional ideals of valuation domains and their duals. These properties are used to prove the conjecture that there is a series of inverses of ideals in a DVR which factors are simple modules over the DVR. The conjecture arises because there is a property which states that every two ideals of valuation domains can be comparable and in addition, these ideals form a series. While there is also another property in PID, that is every ideal of PID has an inverse. By considering more properties of valuation domains and PID it can be proven that the inverses of ideals of DVR can be comparable and form a series which factors are simple modules.

Keywords: dual of ideals discrete valuation domains fractional ideals pid simple modules valuation domains

Published: 2020-02-05
Publisher: EAI

: http://dx.doi.org/10.4108/eai.28-9-2019.2290999