Chinese Journal of Mathematics

Volume 2013, Article ID 570496, 4 pages

http://dx.doi.org/10.1155/2013/570496

## A Note of Filters in Effect Algebras

^{1}Department of Mathematics, Xi’an University of Science and Technology, Xi’an 710054, China^{2}Department of Mathematics, Northwest University, Xi’an 710127, China

Received 29 July 2013; Accepted 23 September 2013

Academic Editors: Z.-Y. Li and C.-s. Liu

Copyright © 2013 Biao Long Meng and Xiao Long Xin. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

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) 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 is an effect algebra filter if and only if is an orthomodular lattice. Every lattice filter in an MV-algebra is an MV-filter if and only if is a Boolean algebra.