… By Proposition (2.1), R is an etale neighbourhood of a localization B of a polynomial algebra
C over A. Le P be a finitely generated projective module over a polynomial Ralgebra R[T], T …

This paper is concerned with the problem of determining those integral domains D which have
the property that finitely generated projective modules over D [X,,..., X,] are extended from …

… He proved in [9]p more generally, that the polynomial ring R[X] with a variable X over …
polynomial ring with a variable X over a Dedekind domain R, then every finite projective R'-module …

The aim of this note is to prove a non-Noetherian generalization of the Serre Conjecture.
However. since we also show that for all zero-dimensional commutative rings R, finitely …

… f1... fmh1...hn ] is a localization of a polynomial ring over a field. Hence projective modules
… Bass on the cancellative nature of large projective modules over polynomial rings, Amer. J. …

… generated projective modules over a polynomial ring with … that finitely generated projective
R[X1,...,Xn]-modules, where … and Simis stating that finitely generated modules over R[X1,...…

… ) division ring, then there exist non-free projective ideals in D … classes of finitely generated
projective modules over D[X, Y ], … a proposition on projective modules over matrix rings and …

… a local ring and R = A[X, X-1] is a Laurent polynomial ring. We prove that for projective Ä-modules
P … We also prove the analogue of the Horrock's theorem for Laurent polynomials rings. …

… In this section we collect some definitions and results for later use; R will denote a commutative
noetherian ring. (2.1) Given a projective R-module P and an element p EP we define O,(p…

… be possible in the polynomial ring case. … for polynomial rings over semilocal rings of positive
dimension. We also establish a theorem on the number of generators of a projective module …