M, ρ, and M/ρ Monoidleri için Sonlu Tam Yeniden Yazma Sistemleri

Year 2023, Volume: 6 Issue: 1, 720 - 725, 10.03.2023

Aykut Emniyet , Basri Çalışkan

https://doi.org/10.47495/okufbed.1093331

Abstract

𝑀 bir monoid ve 𝜌, 𝑀 üzerinde kongrüans olacak biçimde bir denklik bağıntısı olsun. Böylece, 𝜌, 𝑀×𝑀 monoidlerinin direkt çarpımının bir alt monoidi ve 𝑀/𝜌={𝑥𝜌:𝑥∈𝑀} kümesi (𝑥𝜌)(𝑦𝜌)=(𝑥𝑦)𝜌 işlemi ile bir monoid olur. Öncelikle, bir giriş lemması ifade ve ispat edilerek konu ile ilgili bir örnek verilmektedir. Daha sonra, eğer 𝜌 bir sonlu tam yeniden yazma sistemi ile takdim edilebilir ise, 𝑀’nin de bir sonlu tam yeniden yazma sistemi ile takdim edilebilir olduğu gösterilmektedir. Ana sonucun son kısmında, eğer 𝜌 bir sonlu tam yeniden yazma sistemi ile takdim edilebilir ise, 𝑀/𝜌 monoidinin de bir sonlu tam yeniden yazma sistemi ile takdim edilebilir olduğu gösterilmektedir.

Keywords

Yarıgruplar, Monoidler, Takdimler, Kongruanslar, Yeniden Yazma Sistemleri

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

Abstract

Let 𝑀 be a monoid and 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, an introductory lemma is proposed, proved and a relevant example is given. Then, it is shown that if 𝜌 can be presented by a finite complete rewriting system, then so can 𝑀. As the final part of the main result, it is proved that if 𝜌 can be presented by a finite complete rewriting system, then so can 𝑀/𝜌.

Keywords

semigroups, monoids, presentations, congruences, rewriting systems

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