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On a Generalization of the Euclidean Algorithm

Published online by Cambridge University Press:  24 October 2008

P. M. Cohn
P. M. Cohn
Affiliation:
The UniversityManchester 13
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Extract

In any valuated ring R, more specifically, a ring with a degree-function d(a) as defined in §2, the notion of right R-dependence may be denned as follows: (i) The elements a1, …, ar of R are right R-dependent if there exist b1, …, br ∈ R such that . (ii) An element a of R is said to be right R-dependent on the elements a1, …, ar of R if a = 0 or if there exist c1, …, cr ∈ R such that .

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 57 , Issue 1 , January 1961 , pp. 18 - 30
Copyright
Copyright © Cambridge Philosophical Society 1961

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References

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