Stable varieties of semigroups and groupoids

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• 作者：Slavcho Shtrakov ; Jörg Koppitz
• 关键词：Primary ; 08B05 ; Secondary ; 08A02 ; 03C05 ; composition of terms ; essential position in terms ; stable variety
• 刊名：Algebra Universalis
• 出版年：2016
• 出版时间：February 2016
• 年：2016
• 卷：75
• 期：1
• 页码：85-106
• 全文大小：926 KB
• 参考文献：1.Burris, S., Sankappanavar, H.: A Course in universal algebra. The millennium edition. http://​www.​math.​uwaterloo.​ca/​~snburris/​htdocs/​UALG/​univ-algebra2012.​pdf
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  8.Shtrakov S.: Essential variables and positions in terms. Algebra Universalis 61, 381–397 (2009)MathSciNet CrossRef MATH
  
• 作者单位：Slavcho Shtrakov (1)
  Jörg Koppitz (2)
  
  1. Department of Computer Science, South-West University, 2700, Blagoevgrad, Bulgaria
  2. Institute of Mathematics, University of Potsdam, 14415, Potsdam, Germany
  
• 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

The paper deals with \({\sum}\) -composition and \({\sum}\) -essential composition of terms which lead to stable and s-stable varieties of algebras. A full description of all stable varieties of semigroups, commutative and idempotent groupoids is obtained. We use an abstract reduction system which simplifies the presentations of terms of type \({\tau = (2)}\) to study the variety of idempotent groupoids and s-stable varieties of groupoids. S-stable varieties are a variation of stable varieties, used to highlight replacement of subterms of a term in a deductive system instead of the usual replacement of variables by terms. Key words and phrases composition of terms essential position in terms stable variety