{"title":"Sup中的右代数与半单位量子和半积分量子的拓扑表示，再论","authors":"Javier Gutiérrez García, Ulrich Höhle","doi":"10.1515/ms-2024-0020","DOIUrl":null,"url":null,"abstract":"Let 𝔔 be a reduced left-sided and left-stable quantale without zero divisors. This paper shows how the systematic use of the «quantization» of 2 viewed as a regular and strict right 𝔔-subalgebra of 𝔔 can both strengthen and simplify the rather complicated construction of quantale-enriched topologies given for semi-unital and semi-integral quantales in the original paper [3]. The underlying structure for this new construction is an adjoint situation between the dual category of semi-unital, semi-integral quantales and quantized topological spaces.","PeriodicalId":18282,"journal":{"name":"Mathematica Slovaca","volume":"16 1","pages":""},"PeriodicalIF":0.9000,"publicationDate":"2024-05-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Right algebras in Sup and the topological representation of semi-unital and semi-integral quantales, revisited\",\"authors\":\"Javier Gutiérrez García, Ulrich Höhle\",\"doi\":\"10.1515/ms-2024-0020\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Let 𝔔 be a reduced left-sided and left-stable quantale without zero divisors. This paper shows how the systematic use of the «quantization» of 2 viewed as a regular and strict right 𝔔-subalgebra of 𝔔 can both strengthen and simplify the rather complicated construction of quantale-enriched topologies given for semi-unital and semi-integral quantales in the original paper [3]. The underlying structure for this new construction is an adjoint situation between the dual category of semi-unital, semi-integral quantales and quantized topological spaces.\",\"PeriodicalId\":18282,\"journal\":{\"name\":\"Mathematica Slovaca\",\"volume\":\"16 1\",\"pages\":\"\"},\"PeriodicalIF\":0.9000,\"publicationDate\":\"2024-05-28\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Mathematica Slovaca\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1515/ms-2024-0020\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Mathematica Slovaca","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1515/ms-2024-0020","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
Right algebras in Sup and the topological representation of semi-unital and semi-integral quantales, revisited
Let 𝔔 be a reduced left-sided and left-stable quantale without zero divisors. This paper shows how the systematic use of the «quantization» of 2 viewed as a regular and strict right 𝔔-subalgebra of 𝔔 can both strengthen and simplify the rather complicated construction of quantale-enriched topologies given for semi-unital and semi-integral quantales in the original paper [3]. The underlying structure for this new construction is an adjoint situation between the dual category of semi-unital, semi-integral quantales and quantized topological spaces.
期刊介绍：
Mathematica Slovaca, the oldest and best mathematical journal in Slovakia, was founded in 1951 at the Mathematical Institute of the Slovak Academy of Science, Bratislava. It covers practically all mathematical areas. As a respectful international mathematical journal, it publishes only highly nontrivial original articles with complete proofs by assuring a high quality reviewing process. Its reputation was approved by many outstanding mathematicians who already contributed to Math. Slovaca. It makes bridges among mathematics, physics, soft computing, cryptography, biology, economy, measuring, etc. The Journal publishes original articles with complete proofs. Besides short notes the journal publishes also surveys as well as some issues are focusing on a theme of current interest.
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