Test modules for projectivity
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- by P. Jothilingam PDF
- Proc. Amer. Math. Soc. 94 (1985), 593-596 Request permission
Abstract:
Let $R$ be a commutative noetherian local ring with identity. Modules over $R$ will be assumed to be finitely generated and unitary. A nonzero $R$-module $M$ is said to be a strong test module for projectivity if the condition $\operatorname {Ext}_R^1(P,M) = (0)$, for an arbitrary module $P$, implies that $P$ is projective. This definition is due to Mark Ramras [5]. He proves that a necessary condition for $M$ to be a strong test module is that depth $M \leqslant 1$. This is also easy to see. In this note it is proved that, over a regular local ring, this condition is also sufficient for $M$ to qualify as a strong test module.References
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Additional Information
- © Copyright 1985 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 94 (1985), 593-596
- MSC: Primary 13C10; Secondary 13C15
- DOI: https://doi.org/10.1090/S0002-9939-1985-0792267-7
- MathSciNet review: 792267