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Sibirskii Matematicheskii Zhurnal, 2004, Volume 45, Number 3, Pages 558–565 (Mi smj1089)  
Elementary regular rings. II

Yu. L. Ershov

Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences
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Abstract: We extend the well-known result by Burris and Werner on existence of defining sequences for elementary products of models to arbitrary enrichments of Boolean algebras (we obtain a complete analog of the Feferman–Vaught theorem). This enables us to establish decidability of the elementary theory of a classical object of number theory, the ring of adeles.
Keywords: elementary product, defining sequence, elementary regular ring, ring of adeles.
Received: 06.02.2004
English version:
Siberian Mathematical Journal, 2004, Volume 45, Issue 3, Pages 459–464
DOI: https://doi.org/10.1023/B:SIMJ.0000028610.27434.5e
Bibliographic databases:
UDC: 519.4
Language: Russian
Citation: Yu. L. Ershov, “Elementary regular rings. II”, Sibirsk. Mat. Zh., 45:3 (2004), 558–565; Siberian Math. J., 45:3 (2004), 459–464
Citation in format AMSBIB
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