TREED DOMAINS

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International Electronic Journal of Algebra
Volume:3 Issue:3
TREED DOMAINS

TREED DOMAINS

Authors : Gabriel PİCAVET

Pages : 43-57

View : 19 | Download : 11

Publication Date : 2008-06-01

Article Type : Research Paper

Abstract :We establish that treed domains are well behaved in Zafrullah’s sense and have locally polynomial depth 1. For the DW-domains R of Mimouni, such that I−1 6= R for each nontrivial finitely generated ideal I of R, likewise results are proven. We study some special treed domains and show in particular that the Nagata ring of an integral domain R is insert ignore into journalissuearticles values(locally); divided if and only if R is insert ignore into journalissuearticles values(locally); divided and quasi-Prüfer. We show that the small finitistic dimension of a local treed domain is 1 and calculate the small finitistic dimension of localizations of polynomial rings over a treed domain.
Keywords : DW domain, divided domain, going down domain, H domain, idomain, Nagata ring, polynomial, grade, quasi Prüfer domain, small finitistic dimension, t ideal, treed domain, well behaved prime

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