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

Popescu, Dorin

Nagoya Math. J. 113, 121-128 (1989).

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

Keywords:

polynomial algebra; regular ring; Bass-Quillen conjecture; finitely generated projective module

Citations:

Zbl 0477.13006

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