Abstract
Let (R, m) be a local GCD domain. R is called a U2 ring if there is an element u ∈ m − m2 such that R/(u) is a valuation domain and Ru is a Bezout domain. In this case u is called a normal element of R. In this paper we prove that if R is a U2 ring, then R and R[x] are coherent; moreover, if R has a normal element u and dim(R/(u)) = 1, then every finitely generated projective module over R[X] is free.
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