TY - JOUR
T1 - Prüfer v-multiplication domains and related domains of the form D+DS[Γ*]
AU - Chang, Gyu Whan
AU - Kang, Byung Gyun
AU - Lim, Jung Wook
PY - 2010/6
Y1 - 2010/6
N2 - Let D be an integral domain, S be a saturated multiplicative subset of D with D{subset of with not equal to}DS, and Γ be a nonzero torsion-free grading monoid with Γ∩-Γ={0}. Let DS[Γ] be the semigroup ring of Γ over DS, Γ*=Γ-{0}, and D(S,Γ)=D+DS[Γ*], i.e., D(S,Γ)={f∈DS[Γ]|f(0)∈D}. We show that D(S,Γ) is a P. vMD (resp., GCD-domain, GGCD-domain) if and only if D is a P. vMD (resp., GCD-domain, GGCD-domain), Γ is a valuation semigroup and S is a t-splitting (resp., splitting, d-splitting) set of D.
AB - Let D be an integral domain, S be a saturated multiplicative subset of D with D{subset of with not equal to}DS, and Γ be a nonzero torsion-free grading monoid with Γ∩-Γ={0}. Let DS[Γ] be the semigroup ring of Γ over DS, Γ*=Γ-{0}, and D(S,Γ)=D+DS[Γ*], i.e., D(S,Γ)={f∈DS[Γ]|f(0)∈D}. We show that D(S,Γ) is a P. vMD (resp., GCD-domain, GGCD-domain) if and only if D is a P. vMD (resp., GCD-domain, GGCD-domain), Γ is a valuation semigroup and S is a t-splitting (resp., splitting, d-splitting) set of D.
KW - D+D[Γ]
KW - PvMD
KW - T-splitting set
KW - Torsion-free grading monoid Γ with Γ∩-Γ={0}
UR - http://www.scopus.com/inward/record.url?scp=77952290396&partnerID=8YFLogxK
U2 - 10.1016/j.jalgebra.2010.03.010
DO - 10.1016/j.jalgebra.2010.03.010
M3 - Article
AN - SCOPUS:77952290396
SN - 0021-8693
VL - 323
SP - 3124
EP - 3133
JO - Journal of Algebra
JF - Journal of Algebra
IS - 11
ER -