Abstract
In this note, we consider the semigroup O(X) of all order endomorphisms of an infinite chain X and the subset J of O(X) of all transformations alpha such that vertical bar Im(alpha)vertical bar = vertical bar X vertical bar. For an infinite countable chain X, we give a necessary and sufficient condition on X for O(X) = < J > to hold. We also present a sufficient condition on X for O(X) = < J > to hold, for an arbitrary infinite chain X.
Original language | English |
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Article number | 1750031 |
Journal | JOURNAL OF ALGEBRA AND ITS APPLICATIONS |
Volume | 16 |
Issue number | 2 |
DOIs | |
Publication status | Published - Feb 2017 |
Keywords
- Infinite chain
- endomorphism semigroup
- generators
- relative rank