{"title":"与群和半群有关的矩阵","authors":"D.I. Bezushchak","doi":"10.15421/242309","DOIUrl":null,"url":null,"abstract":"Matroid is defined as a pair $(X,\\mathcal{I})$, where $X$ is a nonempty finite set, and $\\mathcal{I}$ is a nonempty set of subsets of $X$ that satisfies the Hereditary Axiom and the Augmentation Axiom. The paper investigates for which semigroups (primarily finite) $S$, the pair $(\\widehat{S}, \\mathcal{I})$ will be a matroid.","PeriodicalId":52827,"journal":{"name":"Researches in Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2023-12-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Matroids related to groups and semigroups\",\"authors\":\"D.I. Bezushchak\",\"doi\":\"10.15421/242309\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Matroid is defined as a pair $(X,\\\\mathcal{I})$, where $X$ is a nonempty finite set, and $\\\\mathcal{I}$ is a nonempty set of subsets of $X$ that satisfies the Hereditary Axiom and the Augmentation Axiom. The paper investigates for which semigroups (primarily finite) $S$, the pair $(\\\\widehat{S}, \\\\mathcal{I})$ will be a matroid.\",\"PeriodicalId\":52827,\"journal\":{\"name\":\"Researches in Mathematics\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2023-12-26\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Researches in Mathematics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.15421/242309\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"Mathematics\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Researches in Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.15421/242309","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"Mathematics","Score":null,"Total":0}
Matroid is defined as a pair $(X,\mathcal{I})$, where $X$ is a nonempty finite set, and $\mathcal{I}$ is a nonempty set of subsets of $X$ that satisfies the Hereditary Axiom and the Augmentation Axiom. The paper investigates for which semigroups (primarily finite) $S$, the pair $(\widehat{S}, \mathcal{I})$ will be a matroid.
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