$\textrm {p.p.}$ 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.References
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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