Hilbert-Kunz theory for binoids
  We develop Hilbert-Kunz theory in a combinatorial setting namely for binoids. We show that the Hilbert-Kunz multiplicity for commutative, finitely generated, semipositive, cancellative and reduced binoids exists and is a rational number. This implies that the corresponding Hilbert-Kunz multiplicity for the binoid algebras does not depend on the characteristic. 
Bayarjargal Batsukh
math.AC