Tbilisi Mathematical Journal

Effective codescent morphisms in the varieties determined by convergent term rewriting systems

Guram Samsonadze and Dali Zangurashvili

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Abstract

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.

Article information

Source
Tbilisi Math. J., Volume 9, Issue 1 (2016), 49-64.

Dates
Received: 24 June 2015
Accepted: 15 December 2015
First available in Project Euclid: 12 June 2018

Permanent link to this document
https://projecteuclid.org/euclid.tbilisi/1528769041

Digital Object Identifier
doi:10.1515/tmj-2016-0005

Mathematical Reviews number (MathSciNet)
MR3461766

Zentralblatt MATH identifier
1337.08004

Subjects
Primary: 08B05: Equational logic, Malʹcev (Malʹtsev) conditions
Secondary: 08B25: Products, amalgamated products, and other kinds of limits and colimits [See also 18A30] 18C20: Algebras and Kleisli categories associated with monads 68Q42: Grammars and rewriting systems

Keywords
Variety of universal algebras normal form for an element of amalgamated free product confluent term rewriting system effective codescent morphism

Citation

Samsonadze, Guram; Zangurashvili, Dali. Effective codescent morphisms in the varieties determined by convergent term rewriting systems. Tbilisi Math. J. 9 (2016), no. 1, 49--64. doi:10.1515/tmj-2016-0005. https://projecteuclid.org/euclid.tbilisi/1528769041


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