{"title":"自由de Morgan代数的函数表示","authors":"Yu. M. Movsisyan","doi":"10.46991/pysu:a/2012.46.3.014","DOIUrl":null,"url":null,"abstract":"It is well known that free Boolean algebra on n free generators is isomorphic to the Boolean algebra of Boolean functions of n variables. The free distributive lattice on n free generators is isomorphic to the lattice of monotone Boolean functions of n variables. In this paper we introduce the concept of De Morgan function and prove that the free De Morgan algebra on n free generators is isomorphic to the De Morgan algebra of De Morgan functions of n variables. Keywords: Antichain, monotone Boolean function, De Morgan function, free De Morgan algebra.","PeriodicalId":21146,"journal":{"name":"Proceedings of the YSU A: Physical and Mathematical Sciences","volume":"91 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2022-01-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"A FUNCTIONAL REPRESENTATION OF FREE DE MORGAN ALGEBRAS\",\"authors\":\"Yu. M. Movsisyan\",\"doi\":\"10.46991/pysu:a/2012.46.3.014\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"It is well known that free Boolean algebra on n free generators is isomorphic to the Boolean algebra of Boolean functions of n variables. The free distributive lattice on n free generators is isomorphic to the lattice of monotone Boolean functions of n variables. In this paper we introduce the concept of De Morgan function and prove that the free De Morgan algebra on n free generators is isomorphic to the De Morgan algebra of De Morgan functions of n variables. Keywords: Antichain, monotone Boolean function, De Morgan function, free De Morgan algebra.\",\"PeriodicalId\":21146,\"journal\":{\"name\":\"Proceedings of the YSU A: Physical and Mathematical Sciences\",\"volume\":\"91 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2022-01-12\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Proceedings of the YSU A: Physical and Mathematical Sciences\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.46991/pysu:a/2012.46.3.014\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Proceedings of the YSU A: Physical and Mathematical Sciences","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.46991/pysu:a/2012.46.3.014","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
A FUNCTIONAL REPRESENTATION OF FREE DE MORGAN ALGEBRAS
It is well known that free Boolean algebra on n free generators is isomorphic to the Boolean algebra of Boolean functions of n variables. The free distributive lattice on n free generators is isomorphic to the lattice of monotone Boolean functions of n variables. In this paper we introduce the concept of De Morgan function and prove that the free De Morgan algebra on n free generators is isomorphic to the De Morgan algebra of De Morgan functions of n variables. Keywords: Antichain, monotone Boolean function, De Morgan function, free De Morgan algebra.
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