CHARACTERIZATIONS OF MV-ALGEBRAS IN TERMS OF CUBIC SETS

Abstract

The operations of cubic sum, cubic product, cubic intersection, cubic union are given in MV-algebras, and the concepts of cubic MV-ideals and cubic prime MV-ideals in MV-algebras are introduced.  Then some characterizations of cubic MV-ideals and cubic prime MV-ideals are obtained.  The image set of cubic prime MV-ideals is proved to be a chain under the order relation \(\preceq\) by discussing the properties of cubic prime ideals, and the cubic prime MV-ideal theory and extension theorem of MV-algebras are presented.  Finally, the quotient structure of cubic MV-ideals is constructed by cubic cosets, and three isomorphism theorems concerning the quotient of cubic MV-ideals are presented by using the notion of invariant cubic sets.