{"title":"异构代数","authors":"Garrett Birkhoff, John D. Lipson","doi":"10.1016/S0021-9800(70)80014-X","DOIUrl":null,"url":null,"abstract":"<div><p>Many of the basic theorems about general “algebras” derived in [1, Ch. 6] are extended to a class of <em>heterogeneous algebras</em> which includes automata, state machines, and monoids acting on sets. It is shown that some algebras can be fruitfully studied, using different interpretations, both as (homogeneous) algebras and as heterogeneous algebras, and a non-trivial “free machine” is constructed as an application. The extent of the overlap with previous work of Higgins [9] is specified.</p></div>","PeriodicalId":100765,"journal":{"name":"Journal of Combinatorial Theory","volume":"8 1","pages":"Pages 115-133"},"PeriodicalIF":0.0000,"publicationDate":"1970-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/S0021-9800(70)80014-X","citationCount":"0","resultStr":"{\"title\":\"Heterogeneous algebras\",\"authors\":\"Garrett Birkhoff, John D. Lipson\",\"doi\":\"10.1016/S0021-9800(70)80014-X\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>Many of the basic theorems about general “algebras” derived in [1, Ch. 6] are extended to a class of <em>heterogeneous algebras</em> which includes automata, state machines, and monoids acting on sets. It is shown that some algebras can be fruitfully studied, using different interpretations, both as (homogeneous) algebras and as heterogeneous algebras, and a non-trivial “free machine” is constructed as an application. The extent of the overlap with previous work of Higgins [9] is specified.</p></div>\",\"PeriodicalId\":100765,\"journal\":{\"name\":\"Journal of Combinatorial Theory\",\"volume\":\"8 1\",\"pages\":\"Pages 115-133\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"1970-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://sci-hub-pdf.com/10.1016/S0021-9800(70)80014-X\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Combinatorial Theory\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S002198007080014X\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Combinatorial Theory","FirstCategoryId":"1085","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S002198007080014X","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Many of the basic theorems about general “algebras” derived in [1, Ch. 6] are extended to a class of heterogeneous algebras which includes automata, state machines, and monoids acting on sets. It is shown that some algebras can be fruitfully studied, using different interpretations, both as (homogeneous) algebras and as heterogeneous algebras, and a non-trivial “free machine” is constructed as an application. The extent of the overlap with previous work of Higgins [9] is specified.
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