Intersection algebras for principal monomial ideals in polynomial rings
Florian Enescu, Sara Malec
TL;DR
This paper investigates the algebraic properties of the intersection algebra of two principal monomial ideals in polynomial rings, focusing on Hilbert series and canonical ideals using diophantine equations.
Contribution
It provides new insights into the structure of intersection algebras of principal monomial ideals, including explicit descriptions of their Hilbert series and canonical ideals.
Findings
Derived formulas for Hilbert series of intersection algebras
Characterized canonical ideals using diophantine equations
Enhanced understanding of algebraic structure of monomial ideal intersections
Abstract
The properties of the intersection algebra of two principal monomial ideals in a polynomial ring are investigated in detail. Results are obtained regarding the Hilbert series and the canonical ideal of the intersection algebra using methods from the theory of diophantine linear equations with integer coefficients.
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