On the structure of the graded algebra associated to a valuation
The main goal of this paper is to study the structure of the graded algebra associated to a valuation. More specifically, we prove that the associated graded algebra grv(R) of a subring (R,m) of a valuation ring Ov, for which Kv:=Ov/mv=R/m, is isomorphic to Kv[tv(R)], where the multiplication is giv...
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| Veröffentlicht in: | Journal of algebra 2020-10, Vol.560, p.667-679 |
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| container_title | Journal of algebra |
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| creator | Barnabé, M.S. Novacoski, J. Spivakovsky, M. |
| description | The main goal of this paper is to study the structure of the graded algebra associated to a valuation. More specifically, we prove that the associated graded algebra grv(R) of a subring (R,m) of a valuation ring Ov, for which Kv:=Ov/mv=R/m, is isomorphic to Kv[tv(R)], where the multiplication is given by a twisting. We show that this twisted multiplication can be chosen to be the usual one in the cases where the value group is free or the residue field is closed by radicals. We also present an example that shows that the isomorphism (with the trivial twisting) does not have to exist. |
| doi_str_mv | 10.1016/j.jalgebra.2020.06.003 |
| format | Article |
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| ispartof | Journal of algebra, 2020-10, Vol.560, p.667-679 |
| issn | 0021-8693 1090-266X |
| language | eng |
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| source | Elsevier ScienceDirect Journals Complete - AutoHoldings; Elektronische Zeitschriftenbibliothek - Frei zugängliche E-Journals |
| subjects | Associated graded ring Mathematics Semigroup algebra Valuations |
| title | On the structure of the graded algebra associated to a valuation |
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