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

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.