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Observables on σ -MV algebras and σ -lattice effect algebras

Anna Jenčová, Sylvia Pulmannová, Elena Vinceková (2011)

Kybernetika

Effect algebras were introduced as abstract models of the set of quantum effects which represent sharp and unsharp properties of physical systems and play a basic role in the foundations of quantum mechanics. In the present paper, observables on lattice ordered σ -effect algebras and their “smearings” with respect to (weak) Markov kernels are studied. It is shown that the range of any observable is contained in a block, which is a σ -MV algebra, and every observable is defined by a smearing of a sharp...

Ojective ideals in modular lattices

Shriram K. Nimbhorkar, Rupal C. Shroff (2015)

Czechoslovak Mathematical Journal

The concept of an extending ideal in a modular lattice is introduced. A translation of module-theoretical concept of ojectivity (i.e. generalized relative injectivity) in the context of the lattice of ideals of a modular lattice is introduced. In a modular lattice satisfying a certain condition, a characterization is given for direct summands of an extending ideal to be mutually ojective. We define exchangeable decomposition and internal exchange property of an ideal in a modular lattice. It is...

On central atoms of Archimedean atomic lattice effect algebras

Martin Kalina (2010)

Kybernetika

If element z of a lattice effect algebra ( E , ⊕ , 0 , 1 ) is central, then the interval [ 0 , z ] is a lattice effect algebra with the new top element z and with inherited partial binary operation ⊕ . It is a known fact that if the set C ( E ) of central elements of E is an atomic Boolean algebra and the supremum of all atoms of C ( E ) in E equals to the top element of E , then E is isomorphic to a direct product of irreducible effect algebras ([16]). In [10] Paseka and Riečanová published as open problem whether C ( E ) is a bifull sublattice...

On centrally symmetric graphs

Manfred Stern (1996)

Mathematica Bohemica

In this note we extend results on the covering graphs of modular lattices (Zelinka) and semimodular lattices (Gedeonova, Duffus and Rival) to the covering graph of certain graded lattices.

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