caa a22 4500 445345144 CHVBK 20180317142826.0 cr unu---uuuuu 170323e20110801xx s 000 0 eng 10.1007/s00233-011-9320-z doi (NATIONALLICENCE)springer-10.1007/s00233-011-9320-z Sanwong Jintana Department of Mathematics, Faculty of Science, Chiang Mai University, 50200, Chiangmai, Thailand aut The regular part of a semigroup of transformations with restricted range [Elektronische Daten] [Jintana Sanwong] Let T(X) be the full transformation semigroup on the set X and let T(X,Y) be the semigroup consisting of all total transformations from X into a fixed subset Y of X. It is known that $$F(X, Y)=\{\alpha\in T(X, Y): X\alpha\subseteq Y\alpha\},$$ is the largest regular subsemigroup of T(X,Y) and determines Green's relations on T(X,Y). In this paper, we show that F(X,Y)≅T(Z) if and only if X=Y and |Y|=|Z|; or |Y|=1=|Z|, and prove that every regular semigroup S can be embedded in F(S 1,S). Then we describe Green's relations and ideals of F(X,Y) and apply these results to get all of its maximal regular subsemigroups when Y is a nonempty finite subset of X. Springer Science+Business Media, LLC, 2011 Transformation semigroup nationallicence Green's relations nationallicence Regular semigroup nationallicence Semigroup Forum Springer-Verlag 83/1(2011-08-01), 134-146 0037-1912 83:1<134 2011 83 233 https://doi.org/10.1007/s00233-011-9320-z text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s00233-011-9320-z text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Sanwong Jintana Department of Mathematics, Faculty of Science, Chiang Mai University, 50200, Chiangmai, Thailand aut NATIONALLICENCE 773 0- Semigroup Forum Springer-Verlag 83/1(2011-08-01), 134-146 0037-1912 83:1<134 2011 83 233 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer