Laterally complete \(C_\infty(Q)\)-modules. (Russian. English summary) Zbl 1448.46040

Chilin, V. I.; Karimov, J. A.

Vladikavkaz. Mat. Zh. 16, No. 2, 69-78 (2014).

Summary: 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 \(\Gamma(X)=\Gamma(Y)\).

MSC:

46H25	Normed modules and Banach modules, topological modules (if not placed in 13-XX or 16-XX)
16D10	General module theory in associative algebras

Keywords:

Hamel \(C_\infty(Q)\)-basis; homogeneous module; \(\sigma\)-finite-dimensional module