20153

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

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

Anahtar Kelimeler:

Yarıgruplar, Monoidler, Takdimler, Kongruanslar, Yeniden Yazma Sistemleri

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

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 (??)(??)=(??)?. 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:

semigroups, monoids, presentations, congruences, rewriting systems,

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