JP Journal of Algebra, Number Theory and Applications
Volume 45, Issue 1, Pages 55 - 66
(January 2020) http://dx.doi.org/10.17654/NT045010055 |
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A FINITENESS CONDITION ON QUASI-LOCAL OVERRINGS OF A CLASS OF PINCHED DOMAINS
Shafiq Ur Rehman, Sehrish Bibi and Rubab Gull
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Abstract: An integral domain is called globalized multiplicatively pinched-Dedekind domain (GMPD domain) if every nonzero non-invertible ideal can be written as with J invertible ideal and distinct ideals which are maximal among the nonzero non-invertible ideals, cf. [2]. The GMPD domains with only finitely many overrings have been recently studied in [15]. In this paper, we find the exact number of quasi-local overrings of GMPD domains having 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. |
Keywords and phrases: overring, localization, integrally closed, Prüfer domain, Dedekind domain, valuation domain, pseudo-valuation domain.
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