Monomial subrings and systems of subintegrality (Q1584039)

Let \(A\) be a subalgebra of \(\mathbb{Z} [t]\) generated by monomials \(b t^n\) for some non-negative integers \(b\) and \(n\). Then \(A\) yields a unique sequence \(\{b_i\}_{i \geq 0}\) of non-negative integers with \(b_i t^i \in A\), and \(b_i\) are the least integers with this property. The authors characterize the sequences for which the corresponding monomial algebra \(A\) is seminormal or weakly normal. They also compute the seminormalization and weak normalization of a given monomial algebra by manipulating the sequences. Illustrative examples are presented throughout, and harder examples are worked out in the last two sections.