Mal’tsev conditions, lack of absorption, and solvability

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• 作者：Libor Barto ; Marcin Kozik ; David Stanovsky
• 关键词：Primary ; 08B05 ; Secondary ; 08A05 ; Mal’tsev condition ; Taylor term ; cube term ; Mal’tsev term ; Taylor variety ; variety with few subpowers ; congruence permutable variety ; congruence meetsemidistributive variety ; absorbing subalgebra ; bin ; absorbing subalgebra ; abelian algebra ; solvable algebra ; affine algebra
• 刊名：Algebra Universalis
• 出版年：2015
• 出版时间：September 2015
• 年：2015
• 卷：74
• 期：1-2
• 页码：185-206
• 全文大小：894 KB
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• 作者单位：Libor Barto (1)
  Marcin Kozik (2)
  David Stanovsky (1)
  
  1. Department of Algebra, Faculty of Mathematics and Physics, Charles University, Sokolovská 83, 18675, Praha 8, Czech Republic
  2. Department of Theoretical Computer Science, Faculty of Mathematics and Computer Science, Jagiellonian University, Golebia 24, Kraków, Poland
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Algebra
  
• 出版者：Birkh盲user Basel
• ISSN：1420-8911

文摘

We provide a new characterization of several Mal’tsev conditions for locally finite varieties using hereditary term properties. We show a particular example of how a lack of absorption causes collapse in the Mal’tsev hierarchy, and point out a connection between solvability and the lack of absorption. As a consequence, we provide a new and conceptually simple proof of a result of Hobby and McKenzie, saying that locally finite varieties with a Taylor term possess a term which is Mal’tsev on blocks of every solvable congruence in every finite algebra in the variety.