×

Polynomial rings and their projective modules. (English) Zbl 0663.13006

Let R be a regular ring. The Bass-Quillen conjecture holds for R if every finitely generated projective module over a polynomial R-algebra R[T], \(T=(T_ 1,...,T_ n)\), \(n\in {\mathbb{N}}\) is extended from R. Here it is shown that the Bass-Quillen conjecture holds for R if either R contains a field or for every prime integer \(p\in {\mathbb{Z}}\) which is not a unit, the ring R/pR is regular. The proof uses H. Lindel’s result [Invent. Math. 65, 319-323 (1981; Zbl 0477.13006)].
Reviewer: D.Popescu

MSC:

13C10 Projective and free modules and ideals in commutative rings
13F20 Polynomial rings and ideals; rings of integer-valued polynomials
13H05 Regular local rings

Citations:

Zbl 0477.13006
PDF BibTeX XML Cite
Full Text: DOI

References:

[1] (1980)
[2] DOI: 10.1007/BF01389017 · Zbl 0477.13006
[3] Publ. Math (1964)
[4] DOI: 10.1090/S0002-9947-1983-0709584-1
[5] Algebraic K-theory II, Lecture Notes in Math. 342 pp 1– (1973)
[6] Nagoya Math. J. 104 pp 85– (1986) · Zbl 0592.14014
[7] Soviet. Math. Dokl. 17 pp 1160– (1976)
[8] DOI: 10.1016/0021-8693(79)90188-1 · Zbl 0437.13003
[9] Lecture Notes in Math. 169 (1970)
[10] DOI: 10.1007/BF01390008 · Zbl 0337.13011
[11] pp 5– (1983)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.