Tail and Free Poset Algebras
Received: September 4, 2002
Accepted: October 22, 2003
We characterize free poset algebras F(P) over partially ordered sets and show that they can be represented by upper semi-lattice algebras. Hence, the uniqueness, in decomposition into normal form, using symmetric difference, of non-zero elements of F(P) is established. Moreover, a characterization of upper semi-lattice algebras that are isomorphic to free poset algebras is given in terms of a selected set of generators of B(T).
Key words: Free poset algebra, tail algebra, semigroup algebra.
2000 Mathematics Subject Classification: Primary: 03G, 06A; Secondary: 06A12,
03G10, 03G05.