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New operations on partial Abelian monoids defined by preideals

Elena Vinceková — 2008

Kybernetika

We consider partial abelian monoids, in particular generalized effect algebras. From the given structures, we construct new ones by introducing a new operation , which is given by restriction of the original partial operation + with respect to a special subset called preideal. We bring some derived properties and characterizations of these new built structures, supporting the results by illustrative examples.

Remarks on effect-tribes

Sylvia PulmannováElena Vinceková — 2015

Kybernetika

We show that an effect tribe of fuzzy sets 𝒯 [ 0 , 1 ] X with the property that every f 𝒯 is 0 ( 𝒯 ) -measurable, where 0 ( 𝒯 ) is the family of subsets of X whose characteristic functions are central elements in 𝒯 , is a tribe. Moreover, a monotone σ -complete effect algebra with RDP with a Loomis-Sikorski representation ( X , 𝒯 , h ) , where the tribe 𝒯 has the property that every f 𝒯 is 0 ( 𝒯 ) -measurable, is a σ -MV-algebra.

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

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...

The exocenter and type decomposition of a generalized pseudoeffect algebra

David J. FoulisSilvia PulmannováElena Vinceková — 2013

Discussiones Mathematicae - General Algebra and Applications

We extend the notion of the exocenter of a generalized effect algebra (GEA) to a generalized pseudoeffect algebra (GPEA) and show that elements of the exocenter are in one-to-one correspondence with direct decompositions of the GPEA; thus the exocenter is a generalization of the center of a pseudoeffect algebra (PEA). The exocenter forms a boolean algebra and the central elements of the GPEA correspond to elements of a sublattice of the exocenter which forms a generalized boolean algebra. We extend...

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