We found a match
Your institution may have access to this item. Find your institution then sign in to continue.
- Title
LOCALLY GCD DOMAINS AND THE RING D + XDS[X].
- Authors
CHANG, G. W.; DUMITRESCU, T.; ZAFRULLAH, M.
- Abstract
An integral domain D is called a locally GCD domain if DM is a GCD domain for every maximal ideal M of D. We study some ringtheoretic properties of locally GCD domains. For example, we show that D is a locally GCD domain if and only if aD ∩ bD is locally principal for all 0 ≠ a; b ∈ D, and at overrings of a locally GCD domain are locally GCD.We also show that the t-class group of a locally GCD domain is just its Picard group. We study when a locally GCD domain is Prüfer or a generalized GCD domain. We also characterize locally factorial domains as domains D whose minimal prime ideals of a nonzero principal ideal are locally principal and discuss conditions that make them Krull domains. We use the D + XDS[X] construction to give some interesting ex- amples of locally GCD domains that are not GCD domains.
- Subjects
INTEGRAL domains; GREATEST common divisor; PICARD groups; PRIME ideals; RING theory; MAXIMAL ideals
- Publication
Bulletin of the Iranian Mathematical Society, 2016, Vol 42, Issue 2, p263
- ISSN
1018-6301
- Publication type
Article