Khaled Alhazmy, Fuad Ali Ahmed Almahdi, Younes El Haddaoui, Najib Mahdou
{"title":"具有有限小有限投影维度的相干环的弱（戈伦斯坦）全局维度","authors":"Khaled Alhazmy, Fuad Ali Ahmed Almahdi, Younes El Haddaoui, Najib Mahdou","doi":"10.1155/2024/4896819","DOIUrl":null,"url":null,"abstract":"The small finitistic dimension of a ring is determined as the supremum projective dimensions among modules with finite projective resolutions. This paper seeks to establish that, for a coherent ring <svg height=\"8.8423pt\" style=\"vertical-align:-0.2064009pt\" version=\"1.1\" viewbox=\"-0.0498162 -8.6359 8.28119 8.8423\" width=\"8.28119pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"><g transform=\"matrix(.013,0,0,-0.013,0,0)\"></path></g></svg> with a finite weak (resp. Gorenstein) global dimension, the small finitistic dimension of <svg height=\"8.8423pt\" style=\"vertical-align:-0.2064009pt\" version=\"1.1\" viewbox=\"-0.0498162 -8.6359 8.28119 8.8423\" width=\"8.28119pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"><g transform=\"matrix(.013,0,0,-0.013,0,0)\"><use xlink:href=\"#g113-83\"></use></g></svg> is equal to its weak (resp. Gorenstein) global dimension. Consequently, we conclude some new characterizations for (Gorenstein) von Neumann and semihereditary rings.","PeriodicalId":54214,"journal":{"name":"Journal of Mathematics","volume":"39 1","pages":""},"PeriodicalIF":1.3000,"publicationDate":"2024-04-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"The Weak (Gorenstein) Global Dimension of Coherent Rings with Finite Small Finitistic Projective Dimension\",\"authors\":\"Khaled Alhazmy, Fuad Ali Ahmed Almahdi, Younes El Haddaoui, Najib Mahdou\",\"doi\":\"10.1155/2024/4896819\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The small finitistic dimension of a ring is determined as the supremum projective dimensions among modules with finite projective resolutions. This paper seeks to establish that, for a coherent ring <svg height=\\\"8.8423pt\\\" style=\\\"vertical-align:-0.2064009pt\\\" version=\\\"1.1\\\" viewbox=\\\"-0.0498162 -8.6359 8.28119 8.8423\\\" width=\\\"8.28119pt\\\" xmlns=\\\"http://www.w3.org/2000/svg\\\" xmlns:xlink=\\\"http://www.w3.org/1999/xlink\\\"><g transform=\\\"matrix(.013,0,0,-0.013,0,0)\\\"></path></g></svg> with a finite weak (resp. Gorenstein) global dimension, the small finitistic dimension of <svg height=\\\"8.8423pt\\\" style=\\\"vertical-align:-0.2064009pt\\\" version=\\\"1.1\\\" viewbox=\\\"-0.0498162 -8.6359 8.28119 8.8423\\\" width=\\\"8.28119pt\\\" xmlns=\\\"http://www.w3.org/2000/svg\\\" xmlns:xlink=\\\"http://www.w3.org/1999/xlink\\\"><g transform=\\\"matrix(.013,0,0,-0.013,0,0)\\\"><use xlink:href=\\\"#g113-83\\\"></use></g></svg> is equal to its weak (resp. Gorenstein) global dimension. Consequently, we conclude some new characterizations for (Gorenstein) von Neumann and semihereditary rings.\",\"PeriodicalId\":54214,\"journal\":{\"name\":\"Journal of Mathematics\",\"volume\":\"39 1\",\"pages\":\"\"},\"PeriodicalIF\":1.3000,\"publicationDate\":\"2024-04-17\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Mathematics\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1155/2024/4896819\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Mathematics","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1155/2024/4896819","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
The Weak (Gorenstein) Global Dimension of Coherent Rings with Finite Small Finitistic Projective Dimension
The small finitistic dimension of a ring is determined as the supremum projective dimensions among modules with finite projective resolutions. This paper seeks to establish that, for a coherent ring with a finite weak (resp. Gorenstein) global dimension, the small finitistic dimension of is equal to its weak (resp. Gorenstein) global dimension. Consequently, we conclude some new characterizations for (Gorenstein) von Neumann and semihereditary rings.
期刊介绍：
Journal of Mathematics is a broad scope journal that publishes original research articles as well as review articles on all aspects of both pure and applied mathematics. As well as original research, Journal of Mathematics also publishes focused review articles that assess the state of the art, and identify upcoming challenges and promising solutions for the community.
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