Ideals $I$ of $R[X]$ for which $R[X]/I$ is $R$-projective
HTML articles powered by AMS MathViewer
- by J. W. Brewer and W. J. Heinzer PDF
- Proc. Amer. Math. Soc. 43 (1974), 21-25 Request permission
Abstract:
A characterization is given of those ideals $I$ of the polynomial ring $R[X]$ such that $R[X]/I$ is $R$-projective. It is also shown that a commutative ring $R$ has the property β$R[X]/IR$-projective implies $I$ is a finitely generated idealβ if and only if $R$ has only a finite number of idempotents.References
-
J. W. Brewer and P. R. Montgomery, The finiteness of $I$ when $R[X]/I$ is $R$-projective, Proc. Amer. Math. (to appear).
- William Heinzer and Jack Ohm, The finiteness of $I$ when $R[X]/I$ is $R$-flat. II, Proc. Amer. Math. Soc. 35 (1972), 1β8. MR 306177, DOI 10.1090/S0002-9939-1972-0306177-3
- Chr. U. Jensen, Homological dimensions of $\aleph _{0}-$coherent rings, Math. Scand. 20 (1967), 55β60. MR 212046, DOI 10.7146/math.scand.a-10819
- Joachim Lambek, Lectures on rings and modules, Blaisdell Publishing Co. [Ginn and Co.], Waltham, Mass.-Toronto, Ont.-London, 1966. With an appendix by Ian G. Connell. MR 0206032
- YΓ΄ichi Miyashita, Commutative Frobenius algebras generated by a single element, J. Fac. Sci. Hokkaido Univ. Ser. I 21 (1970/71), 166β176. MR 0296066
- Jack Ohm and David E. Rush, The finiteness of $I$ when $\textit {R}[\textit {X}]/\textit {I}$ is flat, Trans. Amer. Math. Soc. 171 (1972), 377β408. MR 306176, DOI 10.1090/S0002-9947-1972-0306176-6
- Joseph J. Rotman, Notes on homological algebras, Van Nostrand Reinhold Mathematical Studies, No. 26, Van Nostrand Reinhold Co., New York-Toronto, Ont.-London, 1970. MR 0409590
- Wolmer V. Vasconcelos, Finiteness in projective ideals, J. Algebra 25 (1973), 269β278. MR 314828, DOI 10.1016/0021-8693(73)90045-8
Additional Information
- © Copyright 1974 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 43 (1974), 21-25
- MSC: Primary 13A15
- DOI: https://doi.org/10.1090/S0002-9939-1974-0330130-9
- MathSciNet review: 0330130