Browsing katedra matematiky by Title
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Atomic effect algebras with compression bases
(2011)Compression base effect algebras were recently introduced by Gudder [6]. They generalize sequential effect algebras [7] and compressible effect algebras [5]. The present paper focuses on atomic compression base effect ... 
Atomic Sequential Effect Algebras
(2008)Various conditions ensuring that a sequential effect algebra or the set of sharp elements of a sequential effect algebra is a Boolean algebra are presented. 
Atomistic and orthoatomistic effect algebras
(2008)We characterize atomistic effect algebras, prove that a weakly orthocomplete Archimedean atomic effect algebra is orthoatomistic and present an example of an orthoatomistic orthomodular poset that is not weakly orthocomplete. 
Central Elements of Effect Algebras
(2004) 
Characterizations of spectral automorphisms and a Stonetype theorem in orthomodular lattices
(2011)The notion of spectral automorphism of an orthomodular lattice was introduced by Ivanov and Caragheorgheopol [3] to create an analogue of the Hilbert space spectral theory in the abstract framework of orthomodular lattices. ... 
Common generalizations of orthocomplete and lattice effect algebras
(2010)Connections between the weak orthocompleteness and the maximality property in e ect algebras are presented. It is proved that an orthomodular poset with the maximality property is disjunctive. A characterization of ... 
Commutative Bounded Integral Residuated Orthomodular Lattices are Boolean Algebras
(2011)We show that a commutative bounded integral orthomodular lattice is residuated iff it is a Boolean algebra. This result is a consequence of [7, Theorem 7.31]; however, our proof is independent and uses other instruments. 
Concrete Quantum Logics with Generalised Compatibiliy
(1998)We present three results stating when a concrete (= setrepresentable) quantum logic with covering properties (generalization of compatibility) has to be a Boolean algebra. These results complete and generalize some ... 
Conditions that Force an Orthomodular Poset to Be a Boolean Algebra
(1997)We introduce two new classes of orthomodular posets—the class of weakly Boolean orthomodular posets and the class of orthomodular posets with the property of maximality. The main result of this paper is that the ... 
Effect algebras with the maximality property
(2009)The maximality property was introduced in [9] in orthomodular posets as a common generalization of orthomodular lattices and orthocomplete orthomodular posets. We show that various conditions used in the theory of e ... 
Note on generalizations of orthocomplete and lattice effect algebras
(2011)It is proved that two di erent common generalizations of orthocomplete and lattice e ect algebras coincide within the class of separable Archimedean e ect algebras. 
Triangular Norms with Continous Daigonals
(1999)It is an old open question whether a tnorm with a continuous diagonal must be continuous [7]. We give a partial positive answer for tnorms with noncontinuous additive generators (constructed by the technique of [1, ...