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

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Home Editorial board Publication ethics Peer review guidelines Latest issue All issues Rules for authors Online submission system's guidelines Submit manuscript Contacts Address: Vatutina st. 53, Vladikavkaz, 362025, RNO-A, Russia Phone: (8672)23-00-54 E-mail: rio@smath.ru	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. Abstract: 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 + References 1. Aleksandrov P. S. Vvedenie v Teoriju Mnozhestv i Obshhuju Topologiju, Moskva, Nauka, 1977, 368 p. (Russian). 2. Vladimirov D. A. Bulevy Algebry, Moskva, Nauka, 1969, 319 p. (Russian). 3. Karimov Zh. A. Moduli Kaplanskogo - Gil'berta nad algebroj izmerimyh funkcij. Uzb. Mat. Zhurn., 2010, no. 4, pp. 74-81 (Russian). 4. Kurosh A. G. Kurs Vysshej Algebry, Moskva, Nauka, 1975, 432 p. (Russian). 5. Kusraev A. G. Vektornaja Dvojstvennost' i ee Prilozhenija, Novosibirsk, Nauka, 1985, 256 p. (Russian). 6. Kusraev A. G. Mazhoriruemye Operatory [Dominated Operators], Moskva, Nauka, 2003, 620 p. (Russian). 7. Muratov M. A., Chilin V. I. Algebry izmerimyh i lokal'no izmerimyh operatorov. Tr. In-ta Matematiki NAN Ukrainy, 2007, vol. 69, 307 p. (Russian). 8. Chilin V. I. Partially ordered baer involutive algebras. J. Soviet Mathematics, 1987, vol. 37, no. 6, pp. 1449-1472. 9. Kaplansky J. Projections in Banach algebras. Ann. Math., 1951, vol. 53, pp. 235-249. 10. Kaplansky J. Algebras of type I. Ann. Math., 1952, vol. 56, pp. 450-472. 11. Kaplansky J. Modules over operator algebras. Amer. J. Math., 1953, vol. 75, no. 4, pp. 839-858. The sole copyright holder of the published work is the Founder of the Vladikavkaz Mathematical Journal. The terms of use of this work are governed by an open license (Creative Commons Attribution-NonCommercial 4.0 International). The use of metadata of the scientific article, including the title, abstract, author information, references, identifiers, and other bibliographic description elements for subsequent unrestricted use, is carried out under the terms of the CC BY or CC0 open licenses. ← Contents of issue


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