A Finitely Generated Module over a Valuation Domain

Dwi Mifta Mahanani

Abstract


This article discusses about some properties which are equivalent between a finitely generated module over PID and a finitely generated module over a valuation domain. This can be done by considering a finitely generated module over a DVR. Although in general a PID is not a valuation domain or vice versa, these equivalence of some properties will be valid. It is because a DVR is a PID and a valuation domain at the same time. Those the equivalent properties in a finitely generated module over DVR are related with the decomposition of the module and the height of an element in that module.

Keywords


DVR; finitely generated module; height of element; PID; valuation domain

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References


A.A. Adkins, S.H. Weintraub, "Algebra An Approach via Module Theory", Springer-Verlag,1992.

L. Fuchs, L. Salce, "Modules over Non-Noetherian Domains", Rhode Island: American Mathematical Society, 2001.

L. Salce, P. Zanardo, "Finitely Generated Modules over Valuation Ring". Comm. Algebra. 12:15, pp. 1795-1812. 1984.

Piotr K., Askar A.T., Modules over Discrete Valuation Domains I, Journal of Mathematics Science, Volume 145, No.4, pp. 5008-5048, 2007.




DOI: https://doi.org/10.18860/ca.v6i1.6798

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