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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| Main Authors: | , |
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| Format: | Journal |
| Published: |
2018
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| Online Access: | https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=84880590197&origin=inward http://cmuir.cmu.ac.th/jspui/handle/6653943832/47756 |
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| Institution: | Chiang Mai University |
| Summary: | 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. |
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