{"title":"可加可幂等分线$$S_7^0$$是非无限基于的","authors":"Yanan Wu, Miaomiao Ren, Xianzhong Zhao","doi":"10.1007/s00233-024-10420-2","DOIUrl":null,"url":null,"abstract":"<p>We show that the additively idempotent semiring <span>\\(S_7^0\\)</span> has no finite basis for its equational theory. This answers an open problem posed by Jackson et al. (J Algebra 611:211–245, 2022).</p>","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-03-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"The additively idempotent semiring $$S_7^0$$ is nonfinitely based\",\"authors\":\"Yanan Wu, Miaomiao Ren, Xianzhong Zhao\",\"doi\":\"10.1007/s00233-024-10420-2\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>We show that the additively idempotent semiring <span>\\\\(S_7^0\\\\)</span> has no finite basis for its equational theory. This answers an open problem posed by Jackson et al. (J Algebra 611:211–245, 2022).</p>\",\"PeriodicalId\":0,\"journal\":{\"name\":\"\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0,\"publicationDate\":\"2024-03-20\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1007/s00233-024-10420-2\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s00233-024-10420-2","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
The additively idempotent semiring $$S_7^0$$ is nonfinitely based
We show that the additively idempotent semiring \(S_7^0\) has no finite basis for its equational theory. This answers an open problem posed by Jackson et al. (J Algebra 611:211–245, 2022).
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