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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...

On 0 - 1 measure for projectors

Václav Alda (1980)

Aplikace matematiky

An example of a finite set of projectors in E 3 is exhibited for which no 0-1 measure exists.

On a period of elements of pseudo-BCI-algebras

Grzegorz Dymek (2015)

Discussiones Mathematicae - General Algebra and Applications

The notions of a period of an element of a pseudo-BCI-algebra and a periodic pseudo-BCI-algebra are defined. Some of their properties and characterizations are given.

On a periodic part of pseudo-BCI-algebras

Grzegorz Dymek (2015)

Discussiones Mathematicae - General Algebra and Applications

In the paper the connections between the set of some maximal elements of a pseudo-BCI-algebra and deductive systems are established. Using these facts, a periodic part of a pseudo-BCI-algebra is studied.

On annihilators in BL-algebras

Yu Xi Zou, Xiao Long Xin, Peng Fei He (2016)

Open Mathematics

In the paper, we introduce the notion of annihilators in BL-algebras and investigate some related properties of them. We get that the ideal lattice (I(L), ⊆) is pseudo-complemented, and for any ideal I, its pseudo-complement is the annihilator I⊥ of I. Also, we define the An (L) to be the set of all annihilators of L, then we have that (An(L); ⋂,∧An(L),⊥,0, L) is a Boolean algebra. In addition, we introduce the annihilators of a nonempty subset X of L with respect to an ideal I and study some properties...

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