Finite Complete Rewriting Systems for the Monoids M, Ο, and M/Ο
Aykut Emniyet, Basri ΓALIΕKAN Β· Osmaniye Korkut Ata Γniversitesi Fen Bilimleri EnstitΓΌsΓΌ Dergisi Β· 2023
Let π be a monoid and π be an equivalence relation on π such that π is a congruence. So, π is a submonoid of the direct product of monoids πΓπ, and π/π={π₯π:π₯βπ} is a monoid with the operation (π₯π)(π¦π)=(π₯π¦)π. First, an introductory lemma is proposed, proved and a relevant example is given. Then, it is shown that if π can be presented by a finite complete rewriting system, then so can π. As the final part of the main result, it is proved that if π can be presented by a finite complete rewriting system, then so can π/π.