Geodesic
Endomorphism regular Ockham algebras of finite Boolean type
Glasgow mathematical journal, Tome 39 (1997) no. 1, pp. 99-110

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If (L; ƒ) is an Ockham algebra with dual space (X; g), then it is known that the semigroup of Ockham endomorphisms on L is (anti-)isomorphic to the semigroup Λ(X; g) of continuous order-preserving mappings on X that commute with g. Here we consider the case where L is a finite boolean lattice and ƒ is a bijection. We begin by determining the size of Λ(X;g), and obtain necessary and sufficient conditions for this semigroup to be regular or orthodox. We also describe its structure when it is a group, or an inverse semigroup that is not a group. In the former case it is a cartesian product of cyclic groups and in the latter a cartesian product of cyclic groups each with a zero adjoined. 
Blyth, T. S.; Silva, H. J. Endomorphism regular Ockham algebras of finite Boolean type. Glasgow mathematical journal, Tome 39 (1997) no. 1, pp. 99-110. doi: 10.1017/S0017089500031967
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[1] 1.Blyth, T. S. and Varlet, J. C., Ockham algebras (Oxford Science Publications, Oxford University Press, 1994). Google Scholar | DOI

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