Completeness of the ring of polynomials
Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt
Consider the polynomial ring R:=k[X1,…,Xn]R:=k[X1,…,Xn] in n≥2n≥2 variables over an uncountable field k. We prove that R is complete in its adic topology, that is, the translation invariant topology in which the non-zero ideals form a fundamental system of neighborhoods of 0. In addition we prove that the localization RmRm at a maximal ideal m⊂Rm⊂R is adically complete. The first result settles an old conjecture of C.U. Jensen, the second a conjecture of L. Gruson. Our proofs are based on a result of Gruson stating (in two variables) that RmRm is adically complete when R=k[X1,X2]R=k[X1,X2] and m=(X1,X2)m=(X1,X2).
Originalsprog | Engelsk |
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Tidsskrift | Journal of Pure and Applied Algebra |
Vol/bind | 219 |
Udgave nummer | 4 |
Sider (fra-til) | 1278-1283 |
Antal sider | 6 |
ISSN | 0022-4049 |
DOI | |
Status | Udgivet - 2015 |
ID: 150702861