On semigroups of endomorphisms of a chain with restricted range
Let X be a finite or infinite chain and let {Mathematical expression} be the monoid of all endomorphisms of X. In this paper, we describe the largest regular subsemigroup of {Mathematical expression} and Green's relations on {Mathematical expression}. In fact, more generally, if Y is a nonempty...
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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-s2.0-84887266823&partnerID=40&md5=b976cf83af907df491d5a861d23d66f8 http://cmuir.cmu.ac.th/handle/6653943832/7240 |
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| Institution: | Chiang Mai University |
| Language: | English |
| Summary: | Let X be a finite or infinite chain and let {Mathematical expression} be the monoid of all endomorphisms of X. In this paper, we describe the largest regular subsemigroup of {Mathematical expression} and Green's relations on {Mathematical expression}. In fact, more generally, if Y is a nonempty subset of X and {Mathematical expression} is the subsemigroup of {Mathematical expression} of all elements with range contained in Y, we characterize the largest regular subsemigroup of {Mathematical expression} and Green's relations on {Mathematical expression}. Moreover, for finite chains, we determine when two semigroups of the type {Mathematical expression} are isomorphic and calculate their ranks. © 2013 Springer Science+Business Media New York. |
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