{"title":"相对自由三元体的结构","authors":"A. Zhuchok","doi":"10.12958/ADM1732","DOIUrl":null,"url":null,"abstract":"Loday and Ronco introduced the notions of a~trioid and a trialgebra, and constructed the free trioid of rank 1 and the free trialgebra. This paper is a survey of recent developments in the study of free objects in the varieties of trioids and trialgebras. We present the constructions of the free trialgebra and the free trioid, the free commutative trioid, the free n-nilpotent trioid, the free left (right) n-trinilpotent trioid, and the free rectangular trioid. Some of these results can be applied to constructing relatively free trialgebras.","PeriodicalId":44176,"journal":{"name":"Algebra & Discrete Mathematics","volume":null,"pages":null},"PeriodicalIF":0.3000,"publicationDate":"2021-04-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":"{\"title\":\"Structure of relatively free trioids\",\"authors\":\"A. Zhuchok\",\"doi\":\"10.12958/ADM1732\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Loday and Ronco introduced the notions of a~trioid and a trialgebra, and constructed the free trioid of rank 1 and the free trialgebra. This paper is a survey of recent developments in the study of free objects in the varieties of trioids and trialgebras. We present the constructions of the free trialgebra and the free trioid, the free commutative trioid, the free n-nilpotent trioid, the free left (right) n-trinilpotent trioid, and the free rectangular trioid. Some of these results can be applied to constructing relatively free trialgebras.\",\"PeriodicalId\":44176,\"journal\":{\"name\":\"Algebra & Discrete Mathematics\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.3000,\"publicationDate\":\"2021-04-10\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"2\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Algebra & Discrete Mathematics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.12958/ADM1732\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"MATHEMATICS, APPLIED\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Algebra & Discrete Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.12958/ADM1732","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
Loday and Ronco introduced the notions of a~trioid and a trialgebra, and constructed the free trioid of rank 1 and the free trialgebra. This paper is a survey of recent developments in the study of free objects in the varieties of trioids and trialgebras. We present the constructions of the free trialgebra and the free trioid, the free commutative trioid, the free n-nilpotent trioid, the free left (right) n-trinilpotent trioid, and the free rectangular trioid. Some of these results can be applied to constructing relatively free trialgebras.
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