{"title":"完备格与对合凹上的代数几何","authors":"A. Molkhasi, K. Shum","doi":"10.7151/dmgaa.1394","DOIUrl":null,"url":null,"abstract":"Abstract An involutive pocrim is a resituated integral partially ordered commutative monoid with an involution operator, consider as an algebra. In this paper it is proved that the variety of a finitely generated by involutive pocrims of finite type has a finitely based equational theory. We also study the algebraic geometry over compete lattices and we investigate the properties of being equationally Noetherian and uω-compact over such lattices.","PeriodicalId":36816,"journal":{"name":"Discussiones Mathematicae - General Algebra and Applications","volume":"44 2-3","pages":"339 - 347"},"PeriodicalIF":0.0000,"publicationDate":"2022-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Algebraic Geometry Over Complete Lattices and Involutive Pocrims\",\"authors\":\"A. Molkhasi, K. Shum\",\"doi\":\"10.7151/dmgaa.1394\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Abstract An involutive pocrim is a resituated integral partially ordered commutative monoid with an involution operator, consider as an algebra. In this paper it is proved that the variety of a finitely generated by involutive pocrims of finite type has a finitely based equational theory. We also study the algebraic geometry over compete lattices and we investigate the properties of being equationally Noetherian and uω-compact over such lattices.\",\"PeriodicalId\":36816,\"journal\":{\"name\":\"Discussiones Mathematicae - General Algebra and Applications\",\"volume\":\"44 2-3\",\"pages\":\"339 - 347\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2022-10-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Discussiones Mathematicae - General Algebra and Applications\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.7151/dmgaa.1394\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"Mathematics\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Discussiones Mathematicae - General Algebra and Applications","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.7151/dmgaa.1394","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"Mathematics","Score":null,"Total":0}
Algebraic Geometry Over Complete Lattices and Involutive Pocrims
Abstract An involutive pocrim is a resituated integral partially ordered commutative monoid with an involution operator, consider as an algebra. In this paper it is proved that the variety of a finitely generated by involutive pocrims of finite type has a finitely based equational theory. We also study the algebraic geometry over compete lattices and we investigate the properties of being equationally Noetherian and uω-compact over such lattices.
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