{"title":"Dominions and closed varieties of bands","authors":"Shabnam Abbas, W. Ashraf, N. M. Khan","doi":"10.15672/hujms.1217130","DOIUrl":null,"url":null,"abstract":"In this paper, we improve the results of [1] and solve one of the open problems of [1]. First, we have shown that all subvarieties of the variety of rectangular bands are closed in the variety of n-nilpotent extension of bands. Further, we gave the new, simple and shorter proof of closedness of the variety of regular bands and lastly, we have shown that all subvarieties of the variety of normal bands are closed in the variety of left semiregular bands.","PeriodicalId":55078,"journal":{"name":"Hacettepe Journal of Mathematics and Statistics","volume":"38 1","pages":""},"PeriodicalIF":0.7000,"publicationDate":"2023-05-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Hacettepe Journal of Mathematics and Statistics","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.15672/hujms.1217130","RegionNum":4,"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
Abstract
In this paper, we improve the results of [1] and solve one of the open problems of [1]. First, we have shown that all subvarieties of the variety of rectangular bands are closed in the variety of n-nilpotent extension of bands. Further, we gave the new, simple and shorter proof of closedness of the variety of regular bands and lastly, we have shown that all subvarieties of the variety of normal bands are closed in the variety of left semiregular bands.
期刊介绍：
Hacettepe Journal of Mathematics and Statistics covers all aspects of Mathematics and Statistics. Papers on the interface between Mathematics and Statistics are particularly welcome, including applications to Physics, Actuarial Sciences, Finance and Economics.
We strongly encourage submissions for Statistics Section including current and important real world examples across a wide range of disciplines. Papers have innovations of statistical methodology are highly welcome. Purely theoretical papers may be considered only if they include popular real world applications.
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