turkmath.org

Our main goal is to study the ideal L(P, Q) and toric ring K[P, Q] whose generators are in bijection to the isotone maps from P to Q. We examine the several algebraic properties of L(P, Q) including Alexander duality behaviour. The class of algebras K[P, Q], called isotonian, are natural generalizations of the so-called Hibi rings. We determine the Krull dimension of these algebras and for particular classes of posets P and Q we discuss their normality behaviour. Also, we determine special classes of P and Q for which defining ideal of K[P, Q] admits a quadratic Gröbner basis.