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The Width of a Module

Published online by Cambridge University Press:  20 November 2018

Michael Wichman
Michael Wichman*
Affiliation:
DePaul University, Chicago, Illinois
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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).

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 22 , Issue 1 , 01 February 1970 , pp. 102 - 115
Copyright
Copyright © Canadian Mathematical Society 1970

References

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