Abstract
In Free poset Boolean algebra F(P ), uniqueness of normal form of non-zero elements is proved and the notion of support of a non-zero element is, therefore, well defined. An Inclusion–Exclusion-like formula is given by defining, for each non-zero element x, \(\overline{\mu}(x)\) using support of x ∈F(P ) in a very natural way.
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References
Abraham, U., Bonnet, R., Kubis, W., Rubin, M.: On poset Boolean algebras. Order 20, 265–290 (2004)
Bekkali, M., Zhani, D.: Tail and free poset algebras. Rev. Mat. Complut. 17(1), 169–179 (2004)
Koppelberg, S.: In: Monk, J.D. (ed.) Handbook on Boolean Algebras, vol. 1. North Holland, Amsterdam (1989)
SiKaddour, H.: Ensembles de générateurs d’une algèbre de Boole. Diplôme de Doctorat, Université Claude-Bernard (Lyon 1) (1988)
SiKaddour, H.: A note on the length of members of an interval algebra. Algebra Univers. 44, 195–198 (2000)
Pouzet, M., Rival, I.: Every countable lattice is a retract of a direct product of chains. Algebra Univers. 18, 295–307 (1984)
Zhani, D.: Length of elements in pseudotree algebras. N.Z. J. Math. (2004) (in press)
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Alami, M., Bekkali, M., Faouzi, L. et al. Free poset algebras and combinatorics of cones. Ann Math Artif Intell 49, 15–26 (2007). https://doi.org/10.1007/s10472-007-9058-1
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DOI: https://doi.org/10.1007/s10472-007-9058-1