{"title":"$ \\ mathcal {T} -semiring对美元","authors":"Jaiung Jun, Kalina Mincheva, L. Rowen","doi":"10.14736/kyb-2022-5-0733","DOIUrl":null,"url":null,"abstract":"We develop a general axiomatic theory of algebraic pairs, which simultaneously generalizes several algebraic structures, in order to bypass negation as much as feasible. We investigate several classical theorems and notions in this setting including fractions, integral extensions, and Hilbert's Nullstellensatz. Finally, we study a notion of growth in this context.","PeriodicalId":49928,"journal":{"name":"Kybernetika","volume":"87 1","pages":""},"PeriodicalIF":0.9000,"publicationDate":"2022-03-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"$\\\\mathcal{T}$-semiring pairs\",\"authors\":\"Jaiung Jun, Kalina Mincheva, L. Rowen\",\"doi\":\"10.14736/kyb-2022-5-0733\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We develop a general axiomatic theory of algebraic pairs, which simultaneously generalizes several algebraic structures, in order to bypass negation as much as feasible. We investigate several classical theorems and notions in this setting including fractions, integral extensions, and Hilbert's Nullstellensatz. Finally, we study a notion of growth in this context.\",\"PeriodicalId\":49928,\"journal\":{\"name\":\"Kybernetika\",\"volume\":\"87 1\",\"pages\":\"\"},\"PeriodicalIF\":0.9000,\"publicationDate\":\"2022-03-02\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Kybernetika\",\"FirstCategoryId\":\"94\",\"ListUrlMain\":\"https://doi.org/10.14736/kyb-2022-5-0733\",\"RegionNum\":4,\"RegionCategory\":\"计算机科学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"COMPUTER SCIENCE, CYBERNETICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Kybernetika","FirstCategoryId":"94","ListUrlMain":"https://doi.org/10.14736/kyb-2022-5-0733","RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"COMPUTER SCIENCE, CYBERNETICS","Score":null,"Total":0}
We develop a general axiomatic theory of algebraic pairs, which simultaneously generalizes several algebraic structures, in order to bypass negation as much as feasible. We investigate several classical theorems and notions in this setting including fractions, integral extensions, and Hilbert's Nullstellensatz. Finally, we study a notion of growth in this context.
期刊介绍：
Kybernetika is the bi-monthly international journal dedicated for rapid publication of high-quality, peer-reviewed research articles in fields covered by its title. The journal is published by Nakladatelství Academia, Centre of Administration and Operations of the Czech Academy of Sciences for the Institute of Information Theory and Automation of The Czech Academy of Sciences.
Kybernetika traditionally publishes research results in the fields of Control Sciences, Information Sciences, Statistical Decision Making, Applied Probability Theory, Random Processes, Operations Research, Fuzziness and Uncertainty Theories, as well as in the topics closely related to the above fields.
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