Special elements of the lattice of epigroup varieties

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• 作者：Vyacheslav Yu. Shaprynskiǐ ; Dmitry V. Skokov ; Boris M. Vernikov
• 刊名：Algebra Universalis
• 出版年：2016
• 出版时间：September 2016
• 年：2016
• 卷：76
• 期：1
• 页码：1-30
• 全文大小：1,335 KB
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Algebra
  
• 出版者：Birkh盲user Basel
• ISSN：1420-8911
• 卷排序：76

文摘

We study special elements of three types (namely, neutral, modular and upper-modular elements) in the lattice of all epigroup varieties. Neutral elements are completely determined (it turns out that only four varieties have this property). We find a strong necessary condition for modular elements that completely reduces the problem of description of corresponding varieties to nilvarieties satisfying identities of some special type. Modular elements are completely classified within the class of commutative varieties, while upper-modular elements are completely determined within the wider class of strongly permutative varieties.Key words and phrasesepigroupvariety of epigroupslatticeneutral elementmodular elementupper-modular element