Algebra universalis

, Volume 75, Issue 1, pp 85–106 | Cite as

Stable varieties of semigroups and groupoids

Article

Abstract

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 

2010 Mathematics Subject Classification

Primary: 08B05 Secondary: 08A02 03C05 

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Copyright information

© Springer International Publishing 2015

Authors and Affiliations

  1. 1.Department of Computer ScienceSouth-West UniversityBlagoevgradBulgaria
  2. 2.Institute of MathematicsUniversity of PotsdamPotsdamGermany

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