Some Results on v-Multiplication Rings

Canadian Journal of Mathematics - Tập 19 - Trang 710-722 - 1967
Malcolm Griffin1
1Applied Mathematics Division, D.S.I.R., Wellington, New Zealand

Tóm tắt

A family Ω of valuations of the field K is said to be of finite character if only a finite number of valuations are non-zero at any non-zero element of K. If w ∈ Ω has ring and maximal ideal , then A = ∩w∈Ω is said to be defined by Ω and ∩ A is a prime ideal called the centre of w on A and denoted by Z(w). If = Az(w), then w is said to be an essential valuation for A. A domain defined by a family of finite character in which every valuation is essential is called a ring of Krull type.

Từ khóa


Tài liệu tham khảo

10.1090/S0002-9947-1961-0121405-2

10.1007/978-3-662-29244-0

Griffin Malcolm , Families of finite character and essential valuations (to appear in Trans. Amer. Math. Soc).

Griffin Malcolm , Rings of Krull type (to appear in J. Reine Angew. Math.).

Jaffard, 1960, Les systèmes d'idéaux

10.7146/math.scand.a-10691

Krull, 1935, Ergebnisse der Math., 4

Ribenboim, 1958, Sur les groupes totalement ordonnés et l'arithmétique des anneaux de valuation., Summa Brasil. Math., 4, 1

Zariski, 1958, Commutative algebra,, I

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Canadian Journal of Mathematics

Tập 19

710-722

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