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**Effective codescent morphisms in the varieties determined by convergent term rewriting systems.**
*(English)*
Zbl 1337.08004

Summary: It is shown that the elements of amalgamated free products in a variety of universal algebras have unique normal forms if the variety is represented by a confluent term rewriting system satisfying some additional requirements for its signature and rules. Applying this fact it is proved that any codescent morphism is effective in such varieties. In particular, this is the case for the variety of Mal’tsev algebras, the varieties of magmas with unit and two-sided inverses, idempotent quasigroups, unipotent quasigroups, left Steiner loops, and right Steiner loops.

### MSC:

08B25 | Products, amalgamated products, and other kinds of limits and colimits |

18A20 | Epimorphisms, monomorphisms, special classes of morphisms, null morphisms |

68Q42 | Grammars and rewriting systems |

18C20 | Eilenberg-Moore and Kleisli constructions for monads |

08B05 | Equational logic, Mal’tsev conditions |

08A70 | Applications of universal algebra in computer science |

### Keywords:

varieties of universal algebras; normal forms of elements; amalgamated free products; confluent term rewriting systems; effective codescent morphisms
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\textit{G. Samsonadze} and \textit{D. Zangurashvili}, Tbil. Math. J. 9, No. 1, 49--54 (2016; Zbl 1337.08004)

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