Journal article
The ring D + XDS[X] and t-splitting sets
Arabian Journal for Science and Engineering, Vol.26(1), pp.3-16
2001
Abstract
Let D be an integral domain, S a multiplicatively closed subset of D, and (black star) a finite character star-operation on D. We say that S is a (black star)-splitting set if for each 0 ≠ d ∈ D, there exist integral ideals A and B of D with (d) = (AB)(black star), where A(black star) ∩ sD = sA(black star) for all s ∈ S and B(black star) ∩ S ≠ ∅. We show that D(S) = D + XDS[X] is a PVMD (resp., GGCD domain) if and only if D is a PVMD (resp., GGCD domain) and S is a t-splitting (resp., d-splitting) subset of D. Let S be a t-splitting set of D and let T = {A1 ⋯ An| each Ai, = diDS ∩ D for some nonzero di ∈ D}. Then D = DS ∩ DT. We relate the t-operation on D to the t-operation on DS and DT.
Details
- Title: Subtitle
- The ring D + XDS[X] and t-splitting sets
- Creators
- D.D. AndersonD.F. AndersonM. Zafrullah
- Resource Type
- Journal article
- Publication Details
- Arabian Journal for Science and Engineering, Vol.26(1), pp.3-16
- Publisher
- King Fahd University of Petroleum and Minerals
- ISSN
- 2193-567X
- Language
- English
- Date published
- 2001
- Academic Unit
- Mathematics
- Record Identifier
- 9984230628402771
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