TopologicalStructuresofMV-Algebras

InthispaperweintroducethenotionofatopologicalMV-algebra,I -adic topologyanditscompletion.Someoftheresultsaresimilar tothoseofcommutativeringsbuttheabsenceofadistributivelawconcludethatMV-algebrasarenotringsandrequiresareformulation oftheresultsknowninringtheory.Ifwedenotethecompletionof Aby A thenweprovethatthemap ? : A -? A isinjectiveifandonlyifthetopologyon A isHausdor?.AlsoweprovethatanyMV-algebraA is {0}-adic complete.

کلیدواژه ها:

MV-algebra ، Ideal ، TopologicalMV-algebra ، Completion ، I -adic topology