Abstract
Let X be a chain and OT(X) the full order-preserving transformation semigroup on X. Let Y be a fixed nonempty subset of X and let OT(X, Y) be the subsemigroup of OT(X) of all order-preserving transformations with ranges contained in Y. In this paper, we investigate the order-preserving transformation semigroup
Here, we characterize when an element of OF(X, Y) is regular and describe Green’s relations in OF(X, Y). Moreover, we give a simpler description of Green’s relations, characterize the ideals of OF(X, Y) when Y is a finite subset of X, and apply these results to prove that OF(X, Y) is idempotent generated.
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Presented by J. East.
Dedicated to Brian Davey on the occasion of his 65th birthday
This research was supported by Chiang Mai University.
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Sommanee, W., Sanwong, J. Order-preserving transformations with restricted range: regularity, Green’s relations, and ideals. Algebra Univers. 74, 277–291 (2015). https://doi.org/10.1007/s00012-015-0354-z
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DOI: https://doi.org/10.1007/s00012-015-0354-z