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

		ISSN 1683-3414 (Print) • ISSN 1814-0807 (Online)

Home Editorial board Publication ethics Peer review guidelines Current Archive Rules for authors Contacts Address: Markusa st. 22, Vladikavkaz, 362027, RNO-A, Russia Phone: (8672)50-18-06 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. ← Contents of issue


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