Full paper in PDF:
$% M. Bekkali and D. Zhani, Tail and free poset algebras, Rev. Mat. Complut. 17 (2004), 169179.%$

Tail and Free Poset Algebras

Mohamed BEKKALI and Driss ZHANI
Faculty of Sciences and Technology
P.O.Box 2202
Fez 30000 Morocco
bekka@menara.ma
drisszhani@hotmail.com

Received: September 4, 2002
Accepted: October 22, 2003

 
ABSTRACT

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.