Isotonian Algebras

الأصل · EN

To a pair P and Q of finite posets we attach the toric ring K[P,Q] whose generators are in bijection to the isotone maps from P to Q. This class of algebras, 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 show that K[P,Q] is normal and that their defining ideal admits a quadratic Gröbner basis.