This article is cited in 3 papers

Pure subrings of the rings $\mathbb Z_\chi$

A. V. Tsarev

Moscow State Pedagogical University

Abstract: Pure subrings of finite rank in the $\mathbb Z$-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.

UDC: 512.541+512.552.1+512.553.5

MSC: Primary 13C13; Secondary 20K21, 20K30

Received: 09.04.2008

DOI: 10.4213/sm5235

 English version: Sbornik: Mathematics, 2009, 200:10, 1537–1563

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