Ideals of
for which
is
-projective
Authors:
J. W. Brewer and W. J. Heinzer
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
Full-text PDF Free Access
Abstract | References | Similar Articles | Additional Information
Abstract: A characterization is given of those ideals of the polynomial ring
such that
is
-projective. It is also shown that a commutative ring
has the property ``
-projective implies
is a finitely generated ideal'' if and only if
has only a finite number of idempotents.
- [BM]
J. W. Brewer and P. R. Montgomery, The finiteness of
when
is
-projective, Proc. Amer. Math. (to appear).
- [HO] William Heinzer and Jack Ohm, The finiteness of 𝐼 when 𝑅[𝑋]/𝐼 is 𝑅-flat. II, Proc. Amer. Math. Soc. 35 (1972), 1–8. MR 306177, https://doi.org/10.1090/S0002-9939-1972-0306177-3
- [J] Chr. U. Jensen, Homological dimensions of ℵ₀-coherent rings, Math. Scand. 20 (1967), 55–60. MR 212046, https://doi.org/10.7146/math.scand.a-10819
- [L] Joachim Lambek, Lectures on rings and modules, With an appendix by Ian G. Connell, Blaisdell Publishing Co. Ginn and Co., Waltham, Mass.-Toronto, Ont.-London, 1966. MR 0206032
- [M] Yôichi Miyashita, Commutative Frobenius algebras generated by a single element, J. Fac. Sci. Hokkaido Univ. Ser. I 21 (1970/71), 166–176. MR 0296066
- [OR] Jack Ohm and David E. Rush, The finiteness of 𝐼 when 𝑅[𝑋]/𝐼 is flat, Trans. Amer. Math. Soc. 171 (1972), 377–408. MR 306176, https://doi.org/10.1090/S0002-9947-1972-0306176-6
- [R] Joseph J. Rotman, Notes on homological algebras, Van Nostrand Reinhold Co., New York-Toronto, Ont.-London, 1970. Van Nostrand Reinhold Mathematical Studies, No. 26. MR 0409590
- [V] Wolmer V. Vasconcelos, Finiteness in projective ideals, J. Algebra 25 (1973), 269–278. MR 314828, https://doi.org/10.1016/0021-8693(73)90045-8
Retrieve articles in Proceedings of the American Mathematical Society with MSC: 13A15
Retrieve articles in all journals with MSC: 13A15
Additional Information
DOI:
https://doi.org/10.1090/S0002-9939-1974-0330130-9
Keywords:
Polynomial ring,
projective module,
projective ideal,
content,
finitely generated ideal,
idempotent element
Article copyright:
© Copyright 1974
American Mathematical Society