Crossed product of infinite groups and complete rewriting systems

Çetinalp, Esra Kirmizi; Karpuz, Eylem Güzel

doi:10.3906/mat-2007-9

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2023

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“…FCRSs for matrix semigroup presentations are examined in (Özer and Yüksek, 2016). Authors in (Çetinalp and Karpuz, 2021) studied the solvability of the word problem for infinite groups by obtaining a presentation for the crossed product and then finding its complete rewriting system.…”

Section: Introductionmentioning

confidence: 99%

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

Emniyet

Çalişkan

2023

Osmaniye Korkut Ata Üniversitesi Fen Bilimleri Enstitüsü Dergisi

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In this study, we take M to be a monoid and we let ρ be an equivalence relation on M such that ρ is a congruence. So, ρ is a submonoid of the direct product of monoids M×M, and M/ρ={xρ:x∈M} is a monoid with the operation (xρ)(yρ)=(xy)ρ. First, we propose and prove an introductory lemma and we give a relevant example. Then, we show that if ρ can be presented by a finite complete rewriting system, then so can M. As the final part of our main result, we prove that if ρ can be presented by a finite complete rewriting system, then so can M/ρ.

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Section: Introductionmentioning

confidence: 99%