Local rings of minimal length

被引：6

作者：

Barucci, Valentina ^{[1
]}

机构：

[1] Univ Rome, Dipartimento Matemat, I-00185 Rome, Italy

来源：

JOURNAL OF PURE AND APPLIED ALGEBRA | 2009年 / 213卷 / 06期

关键词：

M-CANONICAL IDEALS; INTEGRAL-DOMAINS;

D O I：

10.1016/j.jpaa.2008.11.007

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This paper deals with local rings R possessing an m-canonical ideal omega, R subset of omega. In particular those rings such that the length I-R(omega/R) is as short as possible are studied. The same notion for one-dimensional local Cohen-Macaulay rings was introduced and studied with the name of Almost Gorenstein. Some necessary conditions, that become also sufficient under additional hypotheses, are given and examples are provided also in the non-Noetherian case. The case when the maximal ideal of R is stable is also studied. (C) 2008 Elsevier B.V. All rights reserved.

引用

页码：991 / 996

页数：6

共 50 条

[21] ON THE LENGTH FORMULA OF HOSKIN AND DELIGNE AND ASSOCIATED GRADED RINGS OF 2-DIMENSIONAL REGULAR LOCAL-RINGS
JOHNSTON, BL
VERMA, J
MATHEMATICAL PROCEEDINGS OF THE CAMBRIDGE PHILOSOPHICAL SOCIETY, 1992, 111 : 423 - 432
[22] MINIMAL BIIDEALS OF RINGS
SZASZ, F
ACTA SCIENTIARUM MATHEMATICARUM, 1971, 32 (3-4): : 333 - &
[23] ON MINIMAL EXTENSIONS OF RINGS
Dorsey, Thomas J.
Mesyan, Zachary
COMMUNICATIONS IN ALGEBRA, 2009, 37 (10) : 3463 - 3486
[24] ON REPRESENTATIONS OF CLASSICAL GROUPS OVER PRINCIPAL IDEAL LOCAL RINGS OF LENGTH TWO
Singla, Pooja
COMMUNICATIONS IN ALGEBRA, 2012, 40 (11) : 4060 - 4067
[25] Minkowski inequality and equality for multiplicity of ideals of finite length in Noetherian local rings
Goel, Kriti
Gurjar, R. V.
Verma, J. K.
CONTRIBUTIONS IN ALGEBRA AND ALGEBRAIC GEOMETRY, 2019, 738 : 33 - 56
[26] ONE-DIMENSIONAL LOCAL-RINGS OF MAXIMAL AND ALMOST MAXIMAL LENGTH
BROWN, WC
HERZOG, J
JOURNAL OF ALGEBRA, 1992, 151 (02) : 332 - 347
[27] MINIMAL RINGS RELATED TO GENERALIZED QUATERNION RINGS
Grau, Jose Maria
Oller-Marcen, Antonio M.
Szabo, Steve
INTERNATIONAL ELECTRONIC JOURNAL OF ALGEBRA, 2023, 34 : 88 - 111
[28] STRUCTURE OF MINIMAL NONCOMMUTATIVE DUO RINGS AND MINIMAL STRONGLY BOUNDED NONDUO RINGS
XUE, WM
COMMUNICATIONS IN ALGEBRA, 1992, 20 (09) : 2777 - 2788
[29] Local rings of exchange rings
Ara, P
Lozano, MG
Molina, MS
COMMUNICATIONS IN ALGEBRA, 1998, 26 (12) : 4191 - 4205
[30] Local Rings of Rings of Quotients
M. A. Gómez Lozano
M. Siles Molina
Algebras and Representation Theory, 2008, 11

← 1 2 3 4 5 →