Abstract:
Pure subrings of finite rank in the Z-adic completion of the ring of integers and in its homomorphic images are considered. Certain properties of these rings are studied (existence of an identity element, decomposability into a direct sum of essentially indecomposable ideals, condition for embeddability into a csp-ring, etc.). Additive groups of these rings and conditions under which these rings are subrings of algebraic number fields are described.
Bibliography: 12 titles.
Keywords:
ring of universal integers, ring of pseudorational numbers, csp-ring, quotient divisible group.
\Bibitem{Tsa09}
\by A.~V.~Tsarev
\paper Pure subrings of the rings $\mathbb Z_\chi$
\jour Sb. Math.
\yr 2009
\vol 200
\issue 10
\pages 1537--1563
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\crossref{https://doi.org/10.1070/SM2009v200n10ABEH004049}
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Linking options:
https://www.mathnet.ru/eng/sm5235
https://doi.org/10.1070/SM2009v200n10ABEH004049
https://www.mathnet.ru/eng/sm/v200/i10/p123
This publication is cited in the following 3 articles:
P. A. Krylov, A. A. Tuganbaev, A. V. Tsarev, “sp-Groups and their endomorphism rings”, J. Math. Sci. (N. Y.), 256:3 (2021), 299–340
O. Guseva, A. V. Tsarev, “Rings whose p-ranks do not exceed 1”, Sb. Math., 205:4 (2014), 476–487
P. A. Krylov, A. A. Tuganbaev, “Idempotent functors and localizations in categories of modules and Abelian groups”, J. Math. Sci., 183:3 (2012), 323–382
Citation in format AMSBIB
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