Regularity in semigroups of transformations with invariant sets
Let T(X) be the semigroup of all transformations on a set X. For a fixed nonempty subset Y of X, let S(X, Y ) = {α ∈ T(X) : Y α ⊆ Y }. Then S(X, Y ) is a semigroup of total transformations on X which leave a subset Y of X invariant. In this paper, we characterize left regular, right regular and intr...
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Journal |
| Published: |
2018
|
| Subjects: | |
| Online Access: | https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=84882965960&origin=inward http://cmuir.cmu.ac.th/jspui/handle/6653943832/52745 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Institution: | Chiang Mai University |
| Summary: | Let T(X) be the semigroup of all transformations on a set X. For a fixed nonempty subset Y of X, let S(X, Y ) = {α ∈ T(X) : Y α ⊆ Y }. Then S(X, Y ) is a semigroup of total transformations on X which leave a subset Y of X invariant. In this paper, we characterize left regular, right regular and intra-regular elements of S(X, Y ) and consider the relationships between these elements. Moreover, we count the number of left regular elements of S(X, Y ) when X is a finite set. © 2013 Academic Publications, Ltd. |
|---|