A note of filters in effect algebras. (Q463172)

Summary: 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.