{"title":"精确多数术语","authors":"Paolo Lipparini","doi":"10.1515/ms-2024-0022","DOIUrl":null,"url":null,"abstract":"We say that an idempotent term <jats:italic>t</jats:italic> is an <jats:italic>exact</jats:italic>-<jats:italic>m</jats:italic>-<jats:italic>majority term</jats:italic> if <jats:italic>t</jats:italic> evaluates to <jats:italic>a</jats:italic>, whenever the element <jats:italic>a</jats:italic> occurs exactly <jats:italic>m</jats:italic> times in the arguments of <jats:italic>t</jats:italic>, and all the other arguments are equal. If <jats:italic>m</jats:italic> < <jats:italic>n</jats:italic> and some variety 𝓥 has an <jats:italic>n</jats:italic>-ary exact-<jats:italic>m</jats:italic>-majority term, then 𝓥 is congruence modular. For certain values of <jats:italic>n</jats:italic> and <jats:italic>m</jats:italic>, for example, <jats:italic>n</jats:italic> = 5 and <jats:italic>m</jats:italic> = 3, the existence of an <jats:italic>n</jats:italic>-ary exact-<jats:italic>m</jats:italic>-majority term neither implies congruence distributivity, nor congruence permutability.","PeriodicalId":18282,"journal":{"name":"Mathematica Slovaca","volume":"48 1","pages":""},"PeriodicalIF":0.9000,"publicationDate":"2024-05-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Exact-m-majority terms\",\"authors\":\"Paolo Lipparini\",\"doi\":\"10.1515/ms-2024-0022\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We say that an idempotent term <jats:italic>t</jats:italic> is an <jats:italic>exact</jats:italic>-<jats:italic>m</jats:italic>-<jats:italic>majority term</jats:italic> if <jats:italic>t</jats:italic> evaluates to <jats:italic>a</jats:italic>, whenever the element <jats:italic>a</jats:italic> occurs exactly <jats:italic>m</jats:italic> times in the arguments of <jats:italic>t</jats:italic>, and all the other arguments are equal. If <jats:italic>m</jats:italic> < <jats:italic>n</jats:italic> and some variety 𝓥 has an <jats:italic>n</jats:italic>-ary exact-<jats:italic>m</jats:italic>-majority term, then 𝓥 is congruence modular. For certain values of <jats:italic>n</jats:italic> and <jats:italic>m</jats:italic>, for example, <jats:italic>n</jats:italic> = 5 and <jats:italic>m</jats:italic> = 3, the existence of an <jats:italic>n</jats:italic>-ary exact-<jats:italic>m</jats:italic>-majority term neither implies congruence distributivity, nor congruence permutability.\",\"PeriodicalId\":18282,\"journal\":{\"name\":\"Mathematica Slovaca\",\"volume\":\"48 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-2024-0022\",\"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-2024-0022","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
摘要
如果元素 a 在 t 的参数中恰好出现了 m 次，并且所有其他参数都相等，那么我们说一个幂项 t 是一个精确-m-多数项。如果 m <n，且某个综项𝓥 有一个 nary 精确-m-多数项，那么𝓥 是全等模态的。对于 n 和 m 的某些值，例如 n = 5 和 m = 3，n-一元精确-m-多数项的存在既不意味着全等可分配性，也不意味着全等可变性。
We say that an idempotent term t is an exact-m-majority term if t evaluates to a, whenever the element a occurs exactly m times in the arguments of t, and all the other arguments are equal. If m < n and some variety 𝓥 has an n-ary exact-m-majority term, then 𝓥 is congruence modular. For certain values of n and m, for example, n = 5 and m = 3, the existence of an n-ary exact-m-majority term neither implies congruence distributivity, nor congruence permutability.
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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