{"title":"磨坊四重奏的和谐之歌","authors":"Hanzhou Lee, J. D. Phillips, Andrew Rajah","doi":"10.1007/s40840-024-01727-y","DOIUrl":null,"url":null,"abstract":"<p>The variety of Moufang loops is axiomatized by any one of four well known (equivalent) identities. We prove that this axiomatic harmony holds in a broader setting by obtaining two alternate, generalized versions of the (traditional) definition of a Moufang loop using four “local” identities, each derived from one of the four “global” Moufang identities, one for loops, the other for magmas with the right or left inverse property.</p>","PeriodicalId":50718,"journal":{"name":"Bulletin of the Malaysian Mathematical Sciences Society","volume":"16 1","pages":""},"PeriodicalIF":1.0000,"publicationDate":"2024-08-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"The Harmonious Song of a Moufang Quartet\",\"authors\":\"Hanzhou Lee, J. D. Phillips, Andrew Rajah\",\"doi\":\"10.1007/s40840-024-01727-y\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>The variety of Moufang loops is axiomatized by any one of four well known (equivalent) identities. We prove that this axiomatic harmony holds in a broader setting by obtaining two alternate, generalized versions of the (traditional) definition of a Moufang loop using four “local” identities, each derived from one of the four “global” Moufang identities, one for loops, the other for magmas with the right or left inverse property.</p>\",\"PeriodicalId\":50718,\"journal\":{\"name\":\"Bulletin of the Malaysian Mathematical Sciences Society\",\"volume\":\"16 1\",\"pages\":\"\"},\"PeriodicalIF\":1.0000,\"publicationDate\":\"2024-08-05\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Bulletin of the Malaysian Mathematical Sciences Society\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1007/s40840-024-01727-y\",\"RegionNum\":3,\"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":"Bulletin of the Malaysian Mathematical Sciences Society","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s40840-024-01727-y","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
The variety of Moufang loops is axiomatized by any one of four well known (equivalent) identities. We prove that this axiomatic harmony holds in a broader setting by obtaining two alternate, generalized versions of the (traditional) definition of a Moufang loop using four “local” identities, each derived from one of the four “global” Moufang identities, one for loops, the other for magmas with the right or left inverse property.
期刊介绍：
This journal publishes original research articles and expository survey articles in all branches of mathematics. Recent issues have included articles on such topics as Spectral synthesis for the operator space projective tensor product of C*-algebras; Topological structures on LA-semigroups; Implicit iteration methods for variational inequalities in Banach spaces; and The Quarter-Sweep Geometric Mean method for solving second kind linear fredholm integral equations.
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