Related papers: Atomistic and orthoatomistic effect algebras
Effect algebras are a generalization of many structures which arise in quantum physics and in mathematical economics. We show that, in every modular Archimedean atomic lattice effect algebra $E$ that is not an orthomodular lattice there…
We study Archimedean atomic lattice effect algebras whose set of sharp elements is a complete lattice. We show properties of centers, compatibility centers and central atoms of such lattice effect algebras. Moreover, we prove that if such…
Special types of effect algebras $E$ called sharply dominating and S-dominating were introduced by S. Gudder in \cite{gudder1,gudder2}. We prove statements about connections between sharp orthocompleteness, sharp dominancy and completeness…
We study observables on monotone $\sigma$-complete effect algebras. We find conditions when a spectral resolution implies existence of the corresponding observable. The set of sharp elements of a monotone $\sigma$-complete homogeneous…
In this paper we characterize the effect algebras whose sharp and principal elements coincide. We also give examples of two non-isomorphic effect algebras having the same universum, partial order and orthosupplementation.
We discuss the relationships between effect algebras with the Riesz Decomposition Property and partially ordered groups with interpolation. We show that any $\sigma$-orthocomplete atomic effect algebra with the Riesz Decomposition Property…
We prove that Archimedean sharply dominating atomic lattice effect algebras can be characterized by property called basic decomposition of elements. As an application we prove the state smearing theorem for these effect algebras.
The aim of our paper is twofold. First, we thoroughly study the set of meager elements Mea(E) and the set of hypermeager elements HMea(E) in the setting of homogeneous effect algebras E. Second, we study the property (W+) and the maximality…
We study equations over boolean algebras with distinguished elements. We prove the criteria, when a boolean algebra is equationally Noetherian, weakly equationally Noetherian, $\mathbf{q}_\omega$-compact or $\mathbf{u}_\omega$-compact. Also…
The maximality property was introduced in in orthomodular posets as a common generalization of orthomodular lattices and orthocomplete orthomodular posets. We show that various conditions used in the theory of effect algebras are stronger…
We introduce a class of monotone $\sigma$-complete effect algebras, called representable, which are $\sigma$-homomorphic images of a class of monotone $\sigma$-complete effect algebras of functions taking values in the interval $[0,1]$ and…
Weakly orthomodular and dually weakly orthomodular lattices were introduced by the authors in a recent paper. Similarly as for orthomodular lattices we try to introduce an implication in these lattices which can be easily axiomatized and…
We give a simple, elementary proof that a uniform algebra is weakly sequentially complete if and only if it is finite-dimensional.
The aim of our paper is twofold. First, we thoroughly study the set of meager elements $M(E)$, the set of sharp elements $S(E)$ and the center $C(E)$ in the setting of meager-orthocomplete homogeneous effect algebras $E$. Second, we prove…
An elegant description of the general form of order automorphisms of effect algebras has been known in the complex case. We present a much simpler proof based on the projective geometry which works also in the real case. As an application…
We prove the result in the title. We infer, that unlike cylindric algebras, there is a first order axiomatization of the class of completely representable polyadic algebras of infinite dimension, though the one we obtain is infinite; in…
Relativization is one of the central topics in the study of algebras of relations. Some relativized relation algebras behave much nicer than the original relation algebras. In this paper, we study the atomicity of the finitely generated…
In this article, we only consider finite effect algebras. We define the concepts of classical and quantum effect algebras and show that an effect algebra $E$ is classical if and only if there exists an observable that measures every effect…
We study atom canonicity for several varieties of cylindric like algebras that contain properly the variety of representable algebras. The algebras in such varieties have relativized representations, and we thereby obtain many omitting…
The aim of our paper is twofold. First, we thoroughly study the set of meager elements M(E), the center C(E) and the compatibility center B(E)in the setting of atomic Archimedean lattice effect algebras E. The main result is that in this…