Geodesic
Defining Families for Integral Domains of Real Finite Character
Canadian journal of mathematics, Tome 24 (1972) no. 6, pp. 1170-1177

Voir la notice de l'article provenant de la source Cambridge University Press

Throughout this paper R and D will denote integral domains with the same quotient field K. A set of integral domains {Di } i∊I with quotient field K will be said to have FC (“finite character” or “finiteness condition“) if 0 ≠ ξ ∊ K implies ξ is a unit of Di for all but finitely many i. If ∩i∊IDi also has quotient field K, then {Di } has FC if and only if every non-zero element in ∩i∊IDi is a non-unit in at most finitely many Di. A non-empty set {Vi}i∊:I of rank one valuation rings with quotient field K will be called a defining family of real R-representativesfor D if {V i} i∊:I has FC, R (⊄ ∩i∊I Vi, and D = R∩ (∩i∊I Vi). 
Heinzer, William; Ohm, Jack. Defining Families for Integral Domains of Real Finite Character. Canadian journal of mathematics, Tome 24 (1972) no. 6, pp. 1170-1177. doi: 10.4153/CJM-1972-125-2
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