{"title":"C 族半群及其诱导有序","authors":"Daniel Marín-Aragón, Raquel Tapia-Ramos","doi":"10.3390/math12182889","DOIUrl":null,"url":null,"abstract":"Let C⊂Np be an integer polyhedral cone. An affine semigroup S⊂C is a C-semigroup if |C∖S|<+∞. This structure has always been studied using a monomial order. The main issue is that the choice of these orders is arbitrary. In the present work, we choose the order given by the semigroup itself, which is a more natural order. This allows us to generalise some of the definitions and results known from numerical semigroup theory to C-semigroups.","PeriodicalId":2,"journal":{"name":"ACS Applied Bio Materials","volume":null,"pages":null},"PeriodicalIF":4.6000,"publicationDate":"2024-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"C-Semigroups and Their Induced Order\",\"authors\":\"Daniel Marín-Aragón, Raquel Tapia-Ramos\",\"doi\":\"10.3390/math12182889\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Let C⊂Np be an integer polyhedral cone. An affine semigroup S⊂C is a C-semigroup if |C∖S|<+∞. This structure has always been studied using a monomial order. The main issue is that the choice of these orders is arbitrary. In the present work, we choose the order given by the semigroup itself, which is a more natural order. This allows us to generalise some of the definitions and results known from numerical semigroup theory to C-semigroups.\",\"PeriodicalId\":2,\"journal\":{\"name\":\"ACS Applied Bio Materials\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":4.6000,\"publicationDate\":\"2024-09-16\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"ACS Applied Bio Materials\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.3390/math12182889\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATERIALS SCIENCE, BIOMATERIALS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"ACS Applied Bio Materials","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.3390/math12182889","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATERIALS SCIENCE, BIOMATERIALS","Score":null,"Total":0}
引用次数: 0
摘要
设 C⊂Np 是一个整数多面体圆锥。如果 |C∖S|<+∞，则仿射半群 S⊂C 是一个 C 半群。对这种结构的研究一直使用单项式阶。主要问题在于这些阶的选择是任意的。在本研究中，我们选择半群本身给出的阶，这是一种更自然的阶。这使我们能够将数字半群理论中的一些定义和结果推广到 C 半群。
Let C⊂Np be an integer polyhedral cone. An affine semigroup S⊂C is a C-semigroup if |C∖S|<+∞. This structure has always been studied using a monomial order. The main issue is that the choice of these orders is arbitrary. In the present work, we choose the order given by the semigroup itself, which is a more natural order. This allows us to generalise some of the definitions and results known from numerical semigroup theory to C-semigroups.
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