Saturation for valuations on two-dimensional regular local rings

被引：22

作者：

Delgado, F ^{[1
]}

Galindo, C

Núñez, A

机构：

[1] Univ Valladolid, Fac Ciencias, Dept Algebra Geometria & Topol, E-47005 Valladolid, Spain

[2] Univ Jaume 1, Dept Matemat, Castellon de La Plana 12071, Spain

来源：

MATHEMATISCHE ZEITSCHRIFT | 2000年 / 234卷 / 03期

关键词：

Geometric Property; Local Ring; Classical Definition; Regular Local Ring; Saturated Ring;

D O I：

10.1007/PL00004811

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We study valuations centered in a regular local ring of dimension two. We define the notion of saturation with respect to such a valuation, extending the classical definitions. The invariants associated in a natural way to the valuation are related with the saturated ring and some geometric properties are deduced.

引用

页码：519 / 550

页数：32

共 50 条

[21] Valuation semigroups of two-dimensional local rings
Cutkosky, Steven Dale
Pham An Vinh
PROCEEDINGS OF THE LONDON MATHEMATICAL SOCIETY, 2014, 108 : 350 - 384
[22] Indecomposable integrally closed modules of rank 3 over two-dimensional regular local rings
Hayasaka, Futoshi
Kodiyalam, Vijay
JOURNAL OF PURE AND APPLIED ALGEBRA, 2024, 228 (06)
[23] The valuative tree of a two-dimensional regular local ring
Granja, A.
MATHEMATICAL RESEARCH LETTERS, 2007, 14 (01) : 19 - 34
[24] NOTE ON INDECOMPOSABLE INTEGRALLY CLOSED MODULES OF RANK 2 OVER TWO-DIMENSIONAL REGULAR LOCAL RINGS
Ayasaka, Futoshi H.
Odiyalam, Vijay K.
JOURNAL OF COMMUTATIVE ALGEBRA, 2023, 15 (04) : 513 - 518
[25] A note on Gersten's conjecture for etale cohomology over two-dimensional henselian regular local rings
Sakagaito, Makoto
COMPTES RENDUS MATHEMATIQUE, 2020, 358 (01) : 33 - 39
[26] A CHARACTERIZATION OF TWO-DIMENSIONAL UNMIXED LOCAL-RINGS
TRUNG, NV
MATHEMATICAL PROCEEDINGS OF THE CAMBRIDGE PHILOSOPHICAL SOCIETY, 1981, 89 (MAR) : 237 - 239
[27] SEPARATION BY VALUATIONS ON REGULAR RINGS OF QUOTIENTS
BROWN, DE
NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY, 1973, 20 (01): : A67 - A67
[28] NONSPLITTING OF VALUATIONS IN EXTENSIONS OF 2 DIMENSIONAL REGULAR LOCAL DOMAINS
ABHYANKA.SS
MATHEMATISCHE ANNALEN, 1967, 170 (02) : 87 - &
[29] A formula for jumping numbers in a two-dimensional regular local ring
Hyry, Eero
Jarvilehto, Tarmo
JOURNAL OF ALGEBRA, 2018, 516 : 437 - 470
[30] The core of a module over a two-dimensional regular local ring
Mohan, R
JOURNAL OF ALGEBRA, 1997, 189 (01) : 1 - 22

← 1 2 3 4 5 →