Lex-ideals of DRl-monoids and GMV-algebras
by
Dana Salounova
Technical University of Ostrava, Czech Republic

The theory of GMV-algebras (or, equivalently, pseudo MV-algebras), as a non-commutative extension of the theory of MV-algebras, has been recently intensively developed. By the representation theorem of Dvurecenskij, every GMV-algebra is isomorphic to a GMV-algebra (which need not be commutative) introduced by a standard method on the unit interval of a unital l-group, and hence the technique of the theory of l-groups is often used also for problems in the theory of GMV-algebras. But this method is limited e.g. by the fact that ideals of GMV-algebras need not be GMV-algebras. Therefore we use another representation of GMV-algebras (in a different signature) in form of special cases of bounded dually residuated l-monoids (DRl-monoids). We study lex-ideals and lex-extensions of DRl-monoids in a large class of bounded DRl-monoids including also GMV-algebras.

Date received: February 28, 2003