Associated Graded Rings and Connected Sums

被引：2

作者：

Ananthnarayan, H. ^{[1
]}

Celikbas, Ela ^{[2
]}

Laxmi, Jai ^{[3
]}

Yang, Zheng ^{[4
]}

机构：

[1] Indian Inst Technol, Dept Math, Main Gate Rd, Mumbai 400076, Maharashtra, India

[2] West Virginia Univ, Dept Math, 94 Beechurst Ave, Morgantown, WV 26505 USA

[3] Univ Connecticut, 341 Mansfield Rd U1009, Storrs, CT 06269 USA

[4] Sichuan Univ, Pittsburgh Inst, Jiangan Campus,Chuanda Rd, Chengdu 610207, Shuangliu Count, Peoples R China

来源：

CZECHOSLOVAK MATHEMATICAL JOURNAL | 2020年 / 70卷 / 01期

关键词：

associated graded ring; fibre product; connected sum; short Gorenstein ring; stretched Gorenstein ring; Poincare series; GORENSTEIN LOCAL-RINGS; POINCARE-SERIES;

D O I：

10.21136/CMJ.2019.0259-18

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In 2012, Ananthnarayan, Avramov and Moore gave a new construction of Gorenstein rings from two Gorenstein local rings, called their connected sum. In this article, we investigate conditions on the associated graded ring of a Gorenstein Artin local ring Q, which force it to be a connected sum over its residue field. In particular, we recover some results regarding short, and stretched, Gorenstein Artin rings. Finally, using these decompositions, we obtain results about the rationality of the Poincare series of Q.

引用

页码：261 / 279

页数：19

共 12 条

[1] Decomposing Gorenstein rings as connected sums
Ananthnarayan, H.
Celikbas, Ela
Laxmi, Jai
Yang, Zheng
[J]. JOURNAL OF ALGEBRA, 2019, 527 : 241 - 263
[2] Connected sums of Gorenstein local rings To Gerson Levin, on his seventieth birthday
Ananthnarayan, H.
Avramov, Luchezar L.
Moore, W. Frank
[J]. JOURNAL FUR DIE REINE UND ANGEWANDTE MATHEMATIK, 2012, 667 : 149 - 176
[3] Ananthnarayan H., 2009, THESIS
[4] POINCARE-SERIES OF MODULES OVER LOCAL-RINGS OF SMALL EMBEDDING CODEPTH OR SMALL LINKING NUMBER
AVRAMOV, LL
KUSTIN, AR
MILLER, M
[J]. JOURNAL OF ALGEBRA, 1988, 118 (01) : 162 - 204
[5] Apolarity and Direct Sum Decomposability of Polynomials
Buczynska, Weronika
Buczynski, Jaroslaw
Kleppe, Johannes
Teitler, Zach
[J]. MICHIGAN MATHEMATICAL JOURNAL, 2015, 64 (04) : 675 - 719
[6] POINCARE SERIES AND DEFORMATIONS OF GORENSTEIN LOCAL ALGEBRAS
Casnati, Gianfranco
Elias, Juan
Notari, Roberto
Rossi, Maria Evelina
[J]. COMMUNICATIONS IN ALGEBRA, 2013, 41 (03) : 1049 - 1059
[7] ISOMORPHISM CLASSES OF SHORT GORENSTEIN LOCAL RINGS VIA MACAULAY'S INVERSE SYSTEM
Elias, J.
Rossi, M. E.
[J]. TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 2012, 364 (09) : 4589 - 4604
[8] Iarrobino A., 1989, Math. Sci. Res. Inst. Publ., V15, P347
[9] Lescot J., 1983, 35 ANN P LECT NOTES, P218
[10] FACTORING OUT THE SOCLE OF A GORENSTEIN RING
LEVIN, GL
AVRAMOV, LL
[J]. JOURNAL OF ALGEBRA, 1978, 55 (01) : 74 - 83

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