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A Theorem on Henselian Rings

Published online by Cambridge University Press:  20 November 2018

N. Sankaran
N. Sankaran*
Affiliation:
Queens University Kingston
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It is known that if K is a field, then the ring of formal power series in one or more variables, with coefficients in K, is Henselian at its maximal ideal. In this note we show that if R is a ring (commutative and with identity element) which is Henselian at the maximal ideals M1, M2, … then R[[x]] - the ring of formal power series in x with coefficients from R - is also Henselian at the maximal ideals M1 ⋅ R[[x]] + x⋅ R[[x]], etc.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 11 , Issue 2 , June 1968 , pp. 275 - 277
Copyright
Copyright © Canadian Mathematical Society 1968

References

1. Lafon, J.P., Anneaux Henselians. (Universite De Montpellier, 1966–1967).Google Scholar
2. Salmon, P., Sur les séries formelles restreintes Bull. Soc. Math. France, 92 (1964) 385-410.Google Scholar