Endomorphisms of the lattice of epigroup varieties

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• 作者：S. V. Gusev ; B. M. Vernikov
• 关键词：Epigroup ; Variety ; Lattice of varieties ; Variety of epigroups of finite degree
• 刊名：Semigroup Forum
• 出版年：2016
• 出版时间：December 2016
• 年：2016
• 卷：93
• 期：3
• 页码：554-574
• 全文大小：519 KB
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Algebra
  
• 出版者：Springer New York
• ISSN：1432-2137
• 卷排序：93

文摘

We consider epigroups as algebras with two operations (multiplication and pseudoinversion) and construct a countably infinite family of injective endomorphisms of the lattice of all epigroup varieties. An epigroup variety is said to be a variety of finite degree if all its nilsemigroups are nilpotent. We characterize epigroup varieties of finite degree in the language of identities and in terms of minimal forbidden subvarieties.