Lexicographic effect algebras

We investigate a class of effect algebras that can be represented in the form Γ(H×→G\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\Gamma (H \overrightarrow{\times} G}$$\end{document}, (u, 0)), where H×→G\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${H \overrightarrow{\times} G}$$\end{document} means the lexicographic product of an Abelian unital po-group (H, u) and an Abelian directed po-group G. We study conditions when an effect algebra is of this form. Fixing a unital po-group (H, u), the category of strongly (H, u)-perfect effect algebras is introduced and it is shown that it is categorically equivalent to the category of directed po-groups with interpolation. We prove some representation theorems of lexicographic effect algebras, including a subdirect product representation by antilattice lexicographic effect algebras.