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DOI: 10.23671/VNC.2016.2.7390

Laterally complete \(C_\infty(Q)\)-modules

Chilin V. I. , Karimov J. A.
Vladikavkaz Mathematical Journal 2014. Vol. 16. Issue 2.
Let \(X\) be a regular laterally complete \(C_\infty(Q)\)-module and \(\mathcal{B}\) be a Boolean algebra whose Stone space is \(Q\). We introduce the passport\(\Gamma(X)\) for \(X\) consisting of uniquely defined partition of unity in  \(\mathcal{B}\) and set of pairwise different cardinal numbers. It is proved that \(C_\infty(Q)\)-modules \(X\) and \(Y\) are isomorphic if and only if \(\Gamma(X) = \Gamma(Y)\).
Keywords: Hamel \(C_\infty(Q)\)-basis, homogeneous module, \(\sigma\)-finite dimensional module
Language: Russian Download the full text  
For citation: Chilin V. I., Karimov J. A. Laterally complete \(C_\infty(Q)\)-modules Vladikavkazskii matematicheskii zhurnal [Vladikavkaz Math. J.], vol. 16, no. 2, pp.69-78. DOI 10.23671/VNC.2016.2.7390
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