Tbilisi Mathematical Journal
- Tbilisi Math. J.
- Volume 9, Issue 1 (2016), 49-64.
Effective codescent morphisms in the varieties determined by convergent term rewriting systems
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.
Tbilisi Math. J., Volume 9, Issue 1 (2016), 49-64.
Received: 24 June 2015
Accepted: 15 December 2015
First available in Project Euclid: 12 June 2018
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
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
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