Facebook Instagram Twitter RSS Feed PodBean Back to top on side

Isometries and direct decompositions of pseudo MV-algebras

In: Mathematica Slovaca, vol. 57, no. 2
Milan Jasem
Detaily:
Rok, strany: 2007, 107 - 118
O článku:
In the paper isometries in pseudo MV-algebras are investigated. It is shown that for every isometry $f$ in a pseudo MV-algebra $\mathcal{A}=(A,\oplus,{}-,{}\sim,0,1)$ there exists an internal direct decomposition $\mathcal{A}=\mathcal{B}0×\mathcal{C}0$ of $\mathcal{A}$ with $\mathcal{C}0$ commutative such that $f(0) = 1C0$ and $f(x) = xB0\oplus(1C0\odot(xC0)-) = xB0\oplus (1C0 - xC0)$ for each $x \in A$. On the other hand, if $\mathcal{A} = \mathcal{P}0× \mathcal{Q}0$ is an internal direct decomposition of a pseudo MV-algebra $\mathcal {A}= (A,\oplus,{}-,{}\sim,0,1)$ with $\mathcal{Q}0$ commutative, then the mapping $g: A \to A$ defined by $g(x) = xP0 \oplus (1Q0 - xQ0)$ is an isometry in $\mathcal{A}$ and $g(0) = 1Q0$.
Ako citovať:
ISO 690:
Jasem, M. 2007. Isometries and direct decompositions of pseudo MV-algebras. In Mathematica Slovaca, vol. 57, no.2, pp. 107-118. 0139-9918.

APA:
Jasem, M. (2007). Isometries and direct decompositions of pseudo MV-algebras. Mathematica Slovaca, 57(2), 107-118. 0139-9918.