Geodesic
The Width of a Module
Canadian journal of mathematics, Tome 22 (1970) no. 1, pp. 102-115

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

An R-module N is said to have finite width n if n is the smallest integer such that for any set of n + 1 elements of N, at least one of the elements is in the submodule generated by the remaining n. The width of N over R will be denoted by W(R, N).The notion of width was introduced by Brameret [2, p. 3605]. However, Cohen [3] investigated rings of finite rank, which, in the case that R is a local Noetherian domain, is equivalent to width (Proposition 1.6). He showed that finite width of R was both equivalent to R having Krull dimension one, and to R having the restricted minimum condition (Theorem 1.12). 
Wichman, Michael. The Width of a Module. Canadian journal of mathematics, Tome 22 (1970) no. 1, pp. 102-115. doi: 10.4153/CJM-1970-013-8
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