@article{ShtrakovKoppitz2016, author = {Shtrakov, Slavcho and Koppitz, J{\"o}rg}, title = {Stable varieties of semigroups and groupoids}, series = {Algebra universalis}, volume = {75}, journal = {Algebra universalis}, publisher = {Springer}, address = {Basel}, issn = {0002-5240}, doi = {10.1007/s00012-015-0359-7}, pages = {85 -- 106}, year = {2016}, abstract = {The paper deals with Sigma-composition and Sigma-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.}, language = {en} }