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arXiv · 1811.09868

A finiteness condition on quasi-local overrings of a class of pinched domains

Shafiq ur Rehman·Sehrish Bibi·Rubab Gull
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Abstract

An integral domain is called {\em Globalized multiplicatively pinched-Dedekind domain $($GMPD domain$)$} if every nonzero non-invertible ideal can be written as $JP_1\cdots P_k$ with $J$ invertible ideal and $P_1,...,P_k$ distinct ideals which are maximal among the nonzero non-invertible ideals, cf. \cite{DumII}. The GMPD domains with only finitely many overrings have been recently studied in \cite{SU}. In this paper we find the exact number of quasi-local overrings of GMPD domains that only finitely many overrings. Also we study the effect of quasi-local overrings on the properties of GMPD domains. Moreover, we consider the structure of the partially ordered set of prime ideals (ordered under inclusion) in a GMPD domain.

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Shafiq ur Rehman, Sehrish Bibi, Rubab Gull. 2019-06-15. A finiteness condition on quasi-local overrings of a class of pinched domains. https://doi.org/10.17654/nt045010055

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