Blocks of homogeneous effect algebras (Q2748269)

An effect algebra is called homogeneous iff \(u\leq v_1\oplus v_2\), \(u\leq (v_1\oplus v_2)'\) imply that \(u=u_1\oplus u_2\) for some \(u_1\leq v_1\), \(u_2\leq v_2\). The author proves that every homogeneous effect algebra is the union of all its maximal MV-subalgebras. This generalizes previous results obtained for special classes of homogeneous effect algebras, namely for lattice effect algebras [\textit{Z. Riečanová}, ``Generalization of blocks for \(D\)-lattices and lattice-ordered effect algebras'', Int. J. Theor. Phys. 39, 231-237 (2000; Zbl 0968.81003)] and orthoalgebras [\textit{J. Hamhalter, M. Navara} and \textit{P. Pták}, ``States on orthoalgebras'', Int. J. Theor. Phys. 34, 1439-1465 (1995; Zbl 0841.03034)]. On the other hand, effect algebras of selfadjoint operators of Hilbert spaces of dimension greater than~1 are not homogeneous.