Defining ideals of affine semigroup rings of codimension 2 (Q1815022)

Let \(A=K[X_1, \dots, X_r]\) be the polynomial ring over a field \(K\). Let \(I\) be the defining ideal for the monoid ring \(A/I\) associated with a submodule of \(\mathbb{Z}^r\) of rank 2. The main result of this paper is that if \(A/I\) is a positively graded \(k\)-Buchsbaum ring and \(I\) has height 2, then \(\mu(I) \leq k+3\). In particular, \(\mu(I) \leq 3\) if \(A/I\) is Cohen-Macaulay, and \(\mu(I) \leq 4\) if \(A/I\) is Buchsbaum.