Abstract
Given a linearly ordered set (A, R ⩽) and an R-monotone function f: A→A, we give a necessary and sufficient condition on A, f, R ⩽, involving generating sets and forbidden subalgebras, for R ⩽ to be a well-ordering.
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References
G.Revesz (1990) When Is a Total Ordering of a Semigroup a Well-Ordering? Semigroup Forum, Vol. 41, pp. 123–126.
J.Szigeti and B.Nagy (1987) Linear extensions of partial orders preserving monotonicity, Order 4, 31–35.
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Communicated by B. Jónsson
Partially supported by Hungarian National Foundation for Scientific Research Grant nr. 1813.
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Szigeti, J. On well-ordered mono-unary algebras. Order 7, 77–81 (1990). https://doi.org/10.1007/BF00383175
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DOI: https://doi.org/10.1007/BF00383175