Perfect linkage of Cohen-Macaulay modules over Cohen-Macaulay rings

被引：6

作者：

Iima, Kei-ichiro ^{[1
]}

Takahashi, Ryo ^{[2
]}

机构：

[1] Nara Coll, Natl Inst Technol, Dept Liberal Studies, 22 Yata Cho, Yamatokoriyarna, Nara 6391080, Japan

[2] Nagoya Univ, Grad Sch Math, Chikusa Ku, Furocho, Nagoya, Aichi 4648602, Japan

来源：

JOURNAL OF ALGEBRA | 2016年 / 458卷

关键词：

CI-linkage; Perfect linkage; Yoshino-Isogawa linkage; Cohen-Macaulay module; Perfect module; Maximal Cohen-Macaulay approximation; MONOMIAL IDEALS; LIAISON CLASSES; GORENSTEIN; CODIMENSION;

D O I：

10.1016/j.jalgebra.2016.03.014

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we introduce and study the notion of linkage by perfect modules, which we call perfect linkage, for Cohen-Macaulay modules over Cohen-Macaulay local rings. We explore perfect linkage in connection with syzygies, maximal Cohen-Macaulay approximations and Yoshino-Isogawa linkage. We recover a theorem of Yoshino and Isogawa, and analyze the structure of double perfect linkage. Moreover, we establish a criterion for two Cohen-Macaulay modules of codimension one to be perfectly linked, and apply it to the classical linkage theory for ideals. We also construct various examples of linkage of modules and ideals. (C) 2016 Published by Elsevier Inc.

引用

页码：134 / 155

页数：22

共 50 条

[1] Linkage of modules over Cohen-Macaulay rings
Dibaei, Mohammad T.
Gheibi, Mohsen
Hassanzadeh, S. H.
Sadeghi, Arash
[J]. JOURNAL OF ALGEBRA, 2011, 335 (01) : 177 - 187
[2] THE STRUCTURE OF BALANCED BIG COHEN-MACAULAY MODULES OVER COHEN-MACAULAY RINGS
Holm, Henrik
[J]. GLASGOW MATHEMATICAL JOURNAL, 2017, 59 (03) : 549 - 561
[3] THE COHEN-MACAULAY TYPE OF COHEN-MACAULAY RINGS
AUSLANDER, M
REITEN, I
[J]. ADVANCES IN MATHEMATICS, 1989, 73 (01) : 1 - 23
[4] Syzygies of Cohen-Macaulay Modules over One Dimensional Cohen-Macaulay Local Rings
Kobayashi, Toshinori
[J]. ALGEBRAS AND REPRESENTATION THEORY, 2022, 25 (05) : 1061 - 1070
[5] QUASI-PERFECT MODULES OVER COHEN-MACAULAY RINGS
FOXBY, HB
[J]. MATHEMATISCHE NACHRICHTEN, 1975, 66 : 103 - 110
[6] PERFECT MODULES OVER COHEN-MACAULAY LOCAL-RINGS
SMOKE, W
[J]. JOURNAL OF ALGEBRA, 1987, 106 (02) : 367 - 375
[7] COHEN-MACAULAY PROPERTIES FOR BALANCED BIG COHEN-MACAULAY MODULES
SHARP, RY
[J]. MATHEMATICAL PROCEEDINGS OF THE CAMBRIDGE PHILOSOPHICAL SOCIETY, 1981, 90 (SEP) : 229 - 238
[8] Graded Cohen-Macaulay rings of wild Cohen-Macaulay type
Drozd, Yuriy A.
Tovpyha, Oleksii
[J]. JOURNAL OF PURE AND APPLIED ALGEBRA, 2014, 218 (09) : 1628 - 1634
[9] The dimension of the category of maximal Cohen-Macaulay modules over Cohen-Macaulay local rings of dimension one
Kawasaki, Takesi
Nakamura, Yukio
Shimada, Kaori
[J]. JOURNAL OF ALGEBRA, 2019, 532 : 8 - 21
[10] Pseudo Cohen-Macaulay and pseudo generalized Cohen-Macaulay modules
Cuong, NT
Nhan, LT
[J]. JOURNAL OF ALGEBRA, 2003, 267 (01) : 156 - 177

← 1 2 3 4 5 →