Semigroups of transformations with fixed sets
Let T (X) denote the semigroup (under composition) of transformations from X into itself. For a fixed subset Y of X, let Fix(X, Y) be the set of all self-maps on X which fix all elements in Y. Then Fix(X, Y) is a regular subsemigroup of T (X). The aim of this paper is to determine the Green's r...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
2014
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| Online Access: | http://www.scopus.com/inward/record.url?eid=2-s2.0-84876029745&partnerID=40&md5=f203d57f7532c81c4612d23e2c1b05e4 http://cmuir.cmu.ac.th/handle/6653943832/7177 |
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| Institution: | Chiang Mai University |
| Language: | English |
| Summary: | Let T (X) denote the semigroup (under composition) of transformations from X into itself. For a fixed subset Y of X, let Fix(X, Y) be the set of all self-maps on X which fix all elements in Y. Then Fix(X, Y) is a regular subsemigroup of T (X). The aim of this paper is to determine the Green's relations and ideals of Fix(X, Y) and prove that Fix(X, Y) is never isomorphic to T (Z) for any set Z when ∅ ≠ Y ⊈ X. However, its rank is related to the rank of T (X\Y) and the cardinality of Y when X is a finite set. © 2013 Copyright NISC Pty Ltd. |
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