戈洛德环上残差域的 Syzygies

arXiv - MATH - Commutative Algebra Pub Date : 2024-08-24 DOI:arxiv-2408.13425

Doan Trung Cuong, Hailong Dao, David Eisenbud, Toshinori Kobayashi, Claudia Polini, Bernd Ulrich

{"title":"戈洛德环上残差域的 Syzygies","authors":"Doan Trung Cuong, Hailong Dao, David Eisenbud, Toshinori Kobayashi, Claudia Polini, Bernd Ulrich","doi":"arxiv-2408.13425","DOIUrl":null,"url":null,"abstract":"Let $(R,m,k)$ be a Golod ring. We show a recurrent formula for high syzygies\nof $k$ interms of previous ones. In the case of embedding dimension at most\n$2$, we provided complete descriptions of all indecomposable summands of all\nsyzygies of $k$.","PeriodicalId":501475,"journal":{"name":"arXiv - MATH - Commutative Algebra","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2024-08-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Syzygies of the residue field over Golod rings\",\"authors\":\"Doan Trung Cuong, Hailong Dao, David Eisenbud, Toshinori Kobayashi, Claudia Polini, Bernd Ulrich\",\"doi\":\"arxiv-2408.13425\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Let $(R,m,k)$ be a Golod ring. We show a recurrent formula for high syzygies\\nof $k$ interms of previous ones. In the case of embedding dimension at most\\n$2$, we provided complete descriptions of all indecomposable summands of all\\nsyzygies of $k$.\",\"PeriodicalId\":501475,\"journal\":{\"name\":\"arXiv - MATH - Commutative Algebra\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-08-24\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"arXiv - MATH - Commutative Algebra\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/arxiv-2408.13425\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - MATH - Commutative Algebra","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2408.13425","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}

引用次数: 0

摘要

让 $(R,m,k)$ 是一个戈罗德环。我们展示了 $k$ 的高对称性相对于之前对称性的重复公式。在嵌入维度最多为 $2$ 的情况下，我们提供了对 $k$ 所有对称性的所有不可分解和子的完整描述。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

Syzygies of the residue field over Golod rings

Let $(R,m,k)$ be a Golod ring. We show a recurrent formula for high syzygies of $k$ interms of previous ones. In the case of embedding dimension at most $2$, we provided complete descriptions of all indecomposable summands of all syzygies of $k$.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

arXiv - MATH - Commutative Algebra

自引率

0.00%

发文量