Purity of monoids and characteristic-free splittings in semigroup rings
Alessandro De Stefani, Jonathan Monta\~no, and Luis, N\'u\~nez-Betancourt
TL;DR
This paper introduces combinatorial invariants for seminormal monoids, linking them to singularities and homological properties of associated semigroup rings, with results that are independent of the characteristic.
Contribution
It develops characteristic-free methods to analyze the purity and singularities of semigroup rings via combinatorial invariants of monoids.
Findings
Established combinatorial invariants relate to singularities
Connected invariants with homological properties of semigroup rings
Results are valid across different characteristics
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.
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Taxonomy
TopicsRings, Modules, and Algebras · Commutative Algebra and Its Applications · semigroups and automata theory