Some homological results on certain finite ring extensions
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- by R. Raphael PDF
- Proc. Amer. Math. Soc. 36 (1972), 331-335 Request permission
Abstract:
All rings are commutative with identity and all modules are unitary. A ring R is connected if 0 and 1 are the only idempotent elements of R. R is semiconnected if the number of idempotents in R is finite. Suppose that R is connected, that I is a principal ideal of $R[x]$, and that $R[x]/I$ is a finitely generated R-module. Then $R[x]/I$ is a free R-module. Suppose that R is semiconnected, that I is a principal ideal of $R[x]$, and that $R[x]/I$ is a finitely generated R-module. Then $R[x]/I$ is a projective R-module. These results are applied to integral extensions.References
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Additional Information
- © Copyright 1972 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 36 (1972), 331-335
- MSC: Primary 13B99
- DOI: https://doi.org/10.1090/S0002-9939-1972-0308103-X
- MathSciNet review: 0308103