On semigroups of endomorphisms of a chain with restricted range

© 2013, Springer Science+Business Media New York. Let X be a finite or infinite chain and let ${\mathcal{O}}(X)$ be the monoid of all endomorphisms of X. In this paper, we describe the largest regular subsemigroup of ${\mathcal{O}}(X)$ and Green’s relations on ${\mathcal{O}}(X)$. In fact, more gener...

وصف كامل

محفوظ في:
التفاصيل البيبلوغرافية
المؤلفون الرئيسيون: Vítor H. Fernandes, Preeyanuch Honyam, Teresa M. Quinteiro, Boorapa Singha
التنسيق: دورية
منشور في: 2018
الوصول للمادة أونلاين:https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=84942193328&origin=inward
http://cmuir.cmu.ac.th/jspui/handle/6653943832/45002
الوسوم: إضافة وسم
لا توجد وسوم, كن أول من يضع وسما على هذه التسجيلة!
المؤسسة: Chiang Mai University
الوصف
الملخص:© 2013, Springer Science+Business Media New York. Let X be a finite or infinite chain and let ${\mathcal{O}}(X)$ be the monoid of all endomorphisms of X. In this paper, we describe the largest regular subsemigroup of ${\mathcal{O}}(X)$ and Green’s relations on ${\mathcal{O}}(X)$. In fact, more generally, if Y is a nonempty subset of X and ${\mathcal{O}}(X,Y)$ is the subsemigroup of ${\mathcal{O}}(X)$ of all elements with range contained in Y, we characterize the largest regular subsemigroup of ${\mathcal{O}}(X,Y)$ and Green’s relations on ${\mathcal{O}}(X,Y)$. Moreover, for finite chains, we determine when two semigroups of the type ${\mathcal {O}}(X,Y)$ are isomorphic and calculate their ranks.