Purity of monoids and characteristic-free splittings in semigroup rings

Abstract

Inspired by methods in prime characteristic in commutative algebra, we introduce and study combinatorial invariants of seminormal monoids. We relate such numbers with the singularities and homological invariants of the semigroup ring associated to the monoid. Our results are characteristic independent.

On Rees algebras of 2‐determinantal ideals

“…In doing so, some of the most common problems involve computing the degrees of the defining relations, measuring the singularities of $${\mathcal {R}}(I)$$, and investigating the Koszulness of $${\mathcal {R}}(I)$$. These avenues of research are very active and we mention some of the more recent papers [2, 3, 5, 9, 14, 18, 30–32, 36].…”