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Free poset algebras and combinatorics of cones
Authors:Mustapha Alami  Mohamed Bekkali  Latifa Faouzi  Driss Zhani
Affiliation:(1) Fez University, P.O. Box 2202, Fez, 30000, Morocco;(2) Fez University, P.O. Box 1796, Fez, 30000, Morocco
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 xF(P ) in a very natural way.
Keywords:Free poset algebras  Interval algebras  Pseudo-tree algebras  Semigroup algebras  Length of element
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