{"title":"免费的半群演讲","authors":"Nwawuru Francis","doi":"10.18063/ijmp.v1i1.671","DOIUrl":null,"url":null,"abstract":"Let and be two free semigroups. We define external direct product of two free semigroups as an ordered pair of words such that and .We investigate the presentations of external direct product of free semigroups, state and prove under some conditions that the external direct product of two finitely generated free semigroups is finitely generated, also the external direct product of two finitely presented free semigroups is finitely presented. ","PeriodicalId":330194,"journal":{"name":"International Journal of Mathematical Physics","volume":"39 2 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2018-07-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"FREE SEMIGROUP PRESENTATIONS\",\"authors\":\"Nwawuru Francis\",\"doi\":\"10.18063/ijmp.v1i1.671\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Let and be two free semigroups. We define external direct product of two free semigroups as an ordered pair of words such that and .We investigate the presentations of external direct product of free semigroups, state and prove under some conditions that the external direct product of two finitely generated free semigroups is finitely generated, also the external direct product of two finitely presented free semigroups is finitely presented. \",\"PeriodicalId\":330194,\"journal\":{\"name\":\"International Journal of Mathematical Physics\",\"volume\":\"39 2 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2018-07-27\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"International Journal of Mathematical Physics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.18063/ijmp.v1i1.671\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"International Journal of Mathematical Physics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.18063/ijmp.v1i1.671","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Let and be two free semigroups. We define external direct product of two free semigroups as an ordered pair of words such that and .We investigate the presentations of external direct product of free semigroups, state and prove under some conditions that the external direct product of two finitely generated free semigroups is finitely generated, also the external direct product of two finitely presented free semigroups is finitely presented.
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