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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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$\textrm {p.p.}$ rings and finitely generated flat ideals
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by Søren Jøndrup PDF
Proc. Amer. Math. Soc. 28 (1971), 431-435 Request permission

Abstract:

In this note all rings considered are associative with an identity element 1 and all modules are unital left modules. It is shown that a commutative ring $R$ has principal ideals projective if and only if $R[X]$ has the same property. Furthermore it is proved that a ring $R$ has all $n$-generated left ideals flat if and only if all $n$-generated right ideals are flat. In the last part of this note we will prove the following results: Fix $n \geqq 1$. Then there exists a ring $R$ such that all $n$-generated left ideals are projective, in particular, flat, while there exists a nonflat $(n + 1)$-generated left ideal.
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Additional Information
  • © Copyright 1971 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 28 (1971), 431-435
  • MSC: Primary 16.20
  • DOI: https://doi.org/10.1090/S0002-9939-1971-0277561-0
  • MathSciNet review: 0277561