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.
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Presented by M. Jackson.
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Shtrakov, S., Koppitz, J. Stable varieties of semigroups and groupoids. Algebra Univers. 75, 85–106 (2016). https://doi.org/10.1007/s00012-015-0359-7
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DOI: https://doi.org/10.1007/s00012-015-0359-7