Rank and idempotent rank of finite full transformation semigroups with restricted range
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 nonempty subset Y of X. In 2011, Sanwong studied the regular part F(X,Y) = {α ∈ T(X,Y):Xα ⊆ Y α}, of T(X,Y) and described its Green's relations...
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th-cmuir.6653943832-70022014-08-30T03:51:28Z Rank and idempotent rank of finite full transformation semigroups with restricted range Sommanee W. Sanwong J. 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 nonempty subset Y of X. In 2011, Sanwong studied the regular part F(X,Y) = {α ∈ T(X,Y):Xα ⊆ Y α}, of T(X,Y) and described its Green's relations and ideals. In this paper, we compute the rank of F(X,Y) when X is a finite set. Moreover, we obtain the rank and idempotent rank of its ideals. © 2013 Springer Science+Business Media New York. 2014-08-30T03:51:28Z 2014-08-30T03:51:28Z 2013 Article 00371912 10.1007/s00233-013-9467-x http://www.scopus.com/inward/record.url?eid=2-s2.0-84880590197&partnerID=40&md5=7599da73ba3d5f8c0a3a2a0388f54aa1 http://cmuir.cmu.ac.th/handle/6653943832/7002 English |
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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 nonempty subset Y of X. In 2011, Sanwong studied the regular part F(X,Y) = {α ∈ T(X,Y):Xα ⊆ Y α}, of T(X,Y) and described its Green's relations and ideals. In this paper, we compute the rank of F(X,Y) when X is a finite set. Moreover, we obtain the rank and idempotent rank of its ideals. © 2013 Springer Science+Business Media New York. |
| format |
Article |
| author |
Sommanee W. Sanwong J. |
| spellingShingle |
Sommanee W. Sanwong J. Rank and idempotent rank of finite full transformation semigroups with restricted range |
| author_facet |
Sommanee W. Sanwong J. |
| author_sort |
Sommanee W. |
| title |
Rank and idempotent rank of finite full transformation semigroups with restricted range |
| title_short |
Rank and idempotent rank of finite full transformation semigroups with restricted range |
| title_full |
Rank and idempotent rank of finite full transformation semigroups with restricted range |
| title_fullStr |
Rank and idempotent rank of finite full transformation semigroups with restricted range |
| title_full_unstemmed |
Rank and idempotent rank of finite full transformation semigroups with restricted range |
| title_sort |
rank and idempotent rank of finite full transformation semigroups with restricted range |
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2014 |
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http://www.scopus.com/inward/record.url?eid=2-s2.0-84880590197&partnerID=40&md5=7599da73ba3d5f8c0a3a2a0388f54aa1 http://cmuir.cmu.ac.th/handle/6653943832/7002 |
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