Abstract
Let R = K[x, y, z] denote the polynomial ring in three variables over an arbitrary field K. We study the factorial closure B(E) of certain R-modules E of projective dimension 1, called monomial modules. The module E is—in a certain sense—related to the defining ideal of a monomial affine space curves in In general, we prove that B(E) is different from Sym R (E). This extends a particular case of an R-module E with this property studied by Samuel [7]. As the main result, we characterize those monomial R-modules E such that B(E) is an R-algebra of finite type and generated in degree 1 and 2 over the symmetric algebra Sym R (E).
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