On isometries in GMV-algebras

Year, pages: 2011, 827 - 833

Let $\mathcal{A}=(A,\oplus,{}^-,{}^\sim,0,1)$ be a GMV-algebra and $ρ: A × A\rightarrow A$ the distance function on $\mathcal{A}$ defined by $ρ(x, y) = (x\vee y) - (x\wedge y)$ for each $x, y\in A$. In this note it is shown that a mapping $f: A \rightarrow A$ such that $ρ(a,b)=ρ(f(a),f(b))$ for each $a,b \in A$ is a bijection and satisfies the following condition $f([c\wedge d,c\vee d])=[f(c)\wedge f(d),f(c)\vee f(d)]$ for each $c,d \in A$.

Jasem, M. 2011. On isometries in GMV-algebras. In Mathematica Slovaca, vol. 61, no.5, pp. 827-833. 0139-9918. DOI: https://doi.org/10.2478/s12175-011-0050-1

Jasem, M. (2011). On isometries in GMV-algebras. Mathematica Slovaca, 61(5), 827-833. 0139-9918. DOI: https://doi.org/10.2478/s12175-011-0050-1