MV-closures of Wajsberg hoops and applications

ABAD, MANUEL; CASTANO, DIEGO NICOLÁS; DÍAZ VARELA, JOSÉ PATRICIO

ALGEBRA UNIVERSALIS

BIRKHAUSER VERLAG AG

Año: 2010 vol. 64 p. 213 - 230

0002-5240

In this paper we construct, given a Wajsberg hoop $mathbf{A}$, an MV-algebra $mathbf{MV(A)}$ such that the underlying set $A$ of $mathbf{A}$ is a maximal filter of $mathbf{MV}(mathbf{A})$ and the quotient $mathbf{MV(A)}/A$ is the two element chain. As an application we provide a topological duality for locally finite Wajsberg hoops based on a previously known duality for locally finite MV-algebras. We also give another duality for $k$-valued Wajsberg hoops based on a different representation of $k$-valued MV-algebras and show the relation to the first duality. We also apply this construction to give a topological representation for free $k$-valued Wajsberg hoops.