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Projective and generating modules over the ring of pseudorational numbers. (English. Russian original) Zbl 1137.16003
Math. Notes 80, No. 3, 417-427 (2006); translation from Mat. Zametki 80, No. 3, 437-448 (2006).
The ring of pseudorational numbers was introduced by A. A. Fomin and P. A. Krylov. In this paper some classes of modules over the ring \(R\) of pseudorational numbers are described.
In particular, the projective \(R\)-modules are characterized and a complete independent system of invariants for projective \(R\)-modules is indicated. An \(R\)-module is flat if and only if it has nonzero elements of finite order. An \(R\)-module \(M\) is generating if and only if \(M\cong R\oplus X\) for some \(R\)-module \(X\).

MSC:
16D40 Free, projective, and flat modules and ideals in associative algebras
13C10 Projective and free modules and ideals in commutative rings
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