Semigroups of transformations with invariant set
Let T(X) denote the semigroup (under composition) of trans-formations from X into itself. For a xed nonempty subset Y of X, let S(X, Y) = {α ε T(X): Y α ⊆ Y} Then S(X, Y) is a semigroup of total transformations of X which leave a subset Y of X invariant. In this paper, we characterize when S(X, Y) i...
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Journal |
| Published: |
2017
|
| Online Access: | https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=79952597964&origin=inward http://cmuir.cmu.ac.th/jspui/handle/6653943832/43082 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Institution: | Chiang Mai University |
| Summary: | Let T(X) denote the semigroup (under composition) of trans-formations from X into itself. For a xed nonempty subset Y of X, let S(X, Y) = {α ε T(X): Y α ⊆ Y} Then S(X, Y) is a semigroup of total transformations of X which leave a subset Y of X invariant. In this paper, we characterize when S(X, Y) is isomorphic to T(Z) for some set Z and prove that every semigroup A can be embedded in S(A 1 ;A). Then we describe Green's relations for S(X, Y) and apply these results to obtain its group H-classes and ideals. © 2011 The Korean Mathematical Society. |
|---|