A note on generators of the endomorphism semigroup of an infinite countable chain
2017 ◽
Vol 16
(02)
◽
pp. 1750031
Keyword(s):
In this note, we consider the semigroup [Formula: see text] of all order endomorphisms of an infinite chain [Formula: see text] and the subset [Formula: see text] of [Formula: see text] of all transformations [Formula: see text] such that [Formula: see text]. For an infinite countable chain [Formula: see text], we give a necessary and sufficient condition on [Formula: see text] for [Formula: see text] to hold. We also present a sufficient condition on [Formula: see text] for [Formula: see text] to hold, for an arbitrary infinite chain [Formula: see text].
2017 ◽
Vol E100.A
(12)
◽
pp. 2764-2775
◽