Finite Complete Rewriting Systems for the Monoids M, ρ, and M/ρ

Authors : Aykut EMNİYET, Basri ÇALIŞKAN

Pages : 720-725

Doi:10.47495/okufbed.1093331

View : 8 | Download : 5

Publication Date : 2023-03-10

Article Type : Research Paper

Abstract :Let ???? be a monoid and ???? be an equivalence relation on ???? such that ???? is a congruence. So, ???? is a submonoid of the direct product of monoids ????×????, and ????/????={????????:????∈????} is a monoid with the operation insert ignore into journalissuearticles values(????????);insert ignore into journalissuearticles values(????????);=insert ignore into journalissuearticles values(????????);????. First, an introductory lemma is proposed, proved and a relevant example is given. Then, it is shown that if ???? can be presented by a finite complete rewriting system, then so can ????. As the final part of the main result, it is proved that if ???? can be presented by a finite complete rewriting system, then so can ????/????.
Keywords : Yarıgruplar, Monoidler, Takdimler, Kongruanslar, Yeniden Yazma Sistemleri