Isometries and direct decompositions of pseudo MV-algebras期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

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Isometries and direct decompositions of pseudo MV-algebras

Authors:	Milan Jasem

Institution:	(1) Department of Mathematics Faculty of Chemical Technology, Slovak Technical University, Radlinského 9, SK-812 37 Bratislava, Slovak Republic

Abstract:	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, ⊕, ⁻, ^∼, 0, 1) there exists an internal direct decomposition $\mathcal{A} = \mathcal{B}^0 \times \mathcal{C}^0$ of $\mathcal{A}$ with $\mathcal{C}^0$ commutative such that $f(0) = 1_{C^0 }$ and $f(x) = x_{B^0 } \oplus (1_{C^0 } \odot (x_{C^0 } )^ - ) = x_{B^0 } \oplus (1_{C^0 } - x_{C^0 } )$ for each x ∈ A. On the other hand, if $\mathcal{A} = \mathcal{P}^0 \times \mathcal{Q}^0$ is an internal direct decomposition of a pseudo MV-algebra $\mathcal{A}$ = (A, ⊕, ⁻, ^∼, 0, 1) with $\mathcal{Q}^0$ commutative, then the mapping g: A → A defined by $g(x) = x_{P^0 } \oplus (1_{Q^0 } - x_{Q^0 } )$ is an isometry in $\mathcal{A}$ and $g(0) = 1_{Q^0 }$ .

Keywords:	pseudo MV-algebra lattice ordered group isometry direct decomposition
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