Prufer v-multiplication domains and related domains of the form D + D-S[Gamma*]
SCIE
SCOPUS
- Title
- Prufer v-multiplication domains and related domains of the form D + D-S[Gamma*]
- Authors
- Chang, GW; Kang, BG; Lim, JW
- Date Issued
- 2010-06-01
- Publisher
- ACADEMIC PRESS INC ELSEVIER SCIENCE
- Abstract
- Let D be an integral domain. S be a saturated multiplicative subset of D with D subset of D-S, and Gamma be a nonzero torsion-free grading monoid with Gamma boolean AND - Gamma = {0}. Let D-S[Gamma] be the semigroup ring of Gamma over D-S, Gamma* = Gamma - {0}, and D-(S,D-Gamma) = D + D-S[Gamma*], i.e., D-(S,D-Gamma) = {f is an element of D-S[Gamma] vertical bar f(0) is an element of D}. We show that D-(S,D-Gamma) is a PvMD (resp., GCD-domain, GGCD-domain) if and only if D is a PvMD (resp., GCD-domain, GGCD-domain), Gamma is a valuation semigroup and S is a t-splitting (resp., splitting, d-splitting) set of D. (C) 2010 Elsevier Inc. All rights reserved.
- Keywords
- Torsion-free grading monoid Gamma with Gamma boolean AND-Gamma = {0}; D + D-S[Gamma*]; PvMD; t-splitting set; GRADED INTEGRAL DOMAIN; T-SPLITTING SETS; CONSTRUCTION; RINGS
- URI
- https://oasis.postech.ac.kr/handle/2014.oak/25707
- DOI
- 10.1016/J.JALGEBRA.2010.03.010
- ISSN
- 0021-8693
- Article Type
- Article
- Citation
- JOURNAL OF ALGEBRA, vol. 323, no. 11, page. 3124 - 3133, 2010-06-01
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