环上有限生成nD行为的状态表示

2015 IEEE 9th International Workshop on Multidimensional (nD) Systems (nDS) Pub Date : 2015-11-23 DOI:10.1109/NDS.2015.7332637

E. Zerz

{"title":"环上有限生成nD行为的状态表示","authors":"E. Zerz","doi":"10.1109/NDS.2015.7332637","DOIUrl":null,"url":null,"abstract":"Multidimensional linear systems that are finite-dimensional over the coefficient field admit 1D-like state space realizations. We generalize this fact to the case where the base field is replaced by an arbitrary commutative Noetherian ring. It turns out that the concept of “state spaces” has to be replaced by that of “state modules”, which are not necessarily free.","PeriodicalId":284922,"journal":{"name":"2015 IEEE 9th International Workshop on Multidimensional (nD) Systems (nDS)","volume":"83 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2015-11-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"State representations of finitely generated nD behaviors over rings\",\"authors\":\"E. Zerz\",\"doi\":\"10.1109/NDS.2015.7332637\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Multidimensional linear systems that are finite-dimensional over the coefficient field admit 1D-like state space realizations. We generalize this fact to the case where the base field is replaced by an arbitrary commutative Noetherian ring. It turns out that the concept of “state spaces” has to be replaced by that of “state modules”, which are not necessarily free.\",\"PeriodicalId\":284922,\"journal\":{\"name\":\"2015 IEEE 9th International Workshop on Multidimensional (nD) Systems (nDS)\",\"volume\":\"83 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2015-11-23\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"2015 IEEE 9th International Workshop on Multidimensional (nD) Systems (nDS)\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1109/NDS.2015.7332637\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"2015 IEEE 9th International Workshop on Multidimensional (nD) Systems (nDS)","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/NDS.2015.7332637","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}

引用次数: 1

摘要

在系数场上有限维的多维线性系统允许类一维状态空间实现。我们将这一事实推广到基域被任意交换诺瑟环所取代的情况。事实证明，“状态空间”的概念必须被“状态模块”所取代，而“状态模块”不一定是自由的。

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

State representations of finitely generated nD behaviors over rings

Multidimensional linear systems that are finite-dimensional over the coefficient field admit 1D-like state space realizations. We generalize this fact to the case where the base field is replaced by an arbitrary commutative Noetherian ring. It turns out that the concept of “state spaces” has to be replaced by that of “state modules”, which are not necessarily free.

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

2015 IEEE 9th International Workshop on Multidimensional (nD) Systems (nDS)

自引率

0.00%

发文量