JP Journal of Algebra, Number Theory and Applications
Volume 31, Issue 1, Pages 15 - 30
(November 2013)
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ABOUT AN EXAMPLE WHERE THE I-ADIC COMPLETION OF A MODULE IS NOT I-ADICALLY COMPLETE
Hamid Kulosman
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Abstract: We discuss the completion of a filtered module M over a not necessarily Noetherian commutative ring R. The main tool that we use is the notion of a standard Cauchy sequence. We pay a special attention to the modules whose I-adic completion is not necessarily I-adically complete. As an example, we find the distances from 0 of every element of the I-adic completion of the -module where K is a field and in the I-adic metric and the metric of the completion. |
Keywords and phrases: I-adic completion, non-Noetherian ring, polynomials, formal power series. |
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