A Note of Filters in Effect Algebras

Abstract EN

We investigate relations of the two classes of filters in effect algebras (resp., MV-algebras).

We prove that a lattice filter in a lattice ordered effect algebra (resp., MV-algebra) E does not need to be an effect algebra filter (resp., MV-filter).

In general, in MV-algebras, every MV-filter is also a lattice filter.

Every lattice filter in a lattice ordered effect algebra E is an effect algebra filter if and only if E is an orthomodular lattice.

Every lattice filter in an MV-algebra E is an MV-filter if and only if E is a Boolean algebra.