Abstract
If one considers a two-sided graded ideal I of a Z-graded ring R, one can construct the completion \({\hat R}\) of R with respect to the I-adic valuation. As R is not a graded ring in general, we are forced to introcuce the graded completion \({{\hat R}^g}\) of R. It is shewn that \({{\hat R}^g}\) can be described by means of a non-Archimedean uniforÂmity, which is not necessarily metrizable. Also relations with the completeness properties of Ro are studied. In the last section, we study the notion of gr-Henselian rings. It turns out that a gr-local ring R is gr-Henselian if and only if Ro is Henselian. Also a graded version of Henselian lemma is presented.
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© 1984 D. Reidel Publishing Company
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Caenepeel, S. (1984). Graded Complete and Graded Henselian Rings. In: van Oystaeyen, F. (eds) Methods in Ring Theory. NATO ASI Series, vol 129. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-6369-6_4
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DOI: https://doi.org/10.1007/978-94-009-6369-6_4
Publisher Name: Springer, Dordrecht
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