Special Semigroup Classes Over Some Monoid Constructions and a New Example of a Finitely Presented Monoid with a Non-Finitely Generated Group of Units

Authors : Seda OĞUZ ÜNAL

Pages : 303-313

View : 53 | Download : 14

Publication Date : 2016-10-20

Article Type : Other Papers

Abstract :Abstract . In this paper, necessary and sufficient conditions are studied for Bruck-Reilly and gener- alized Bruck-Reilly ∗-extensions of direct product of k monoids to be regular, unit regular, completely regular and orthodox. Moreover, we give an example of a finitely presented monoid (generalized Bruck-Reilly ∗-extension of Bruck-Reilly extension of a free group with infinite rank), the group of units of which is not finitely generated. 2010 Mathematics Subject Classification: 16S15; 20E06; 20E22. Keywords and Phrases: Generalized Bruck-Reilly ∗-extension, finite generation, finite presentability.   Özet.   Bu makalede k tane monoidin direkt çarpımının Bruck-Reilly ve genelleştirilmiş Bruck-Reilly *- genişlemelerinin, regüler, terslenebilir regüler, tamamen regüler ve orthodox olabilmesi için gerek ve yeter koşullar çalışılmıştır.  Ayrıca, biz terslenebilir elemanlarının grubu sonlu üreteçli olmayan sonlu sunumlu bir monoid (sonsuz ranklı bir serbest grubun Bruck-Reilly genişlemesinin genelleştirilmiş Bruck-Reilly *-genişlemesi) örneği verdik.   Anahtar Kelimeler: Genelleştirilmiş Bruck-Reilly *-genişlemesi, sonlu üreteçlilik, sonlu sunumluluk.
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