Bigdeli, Mina and Herzog, Jürgen and Hibi, Takayuki and Qureshi, Ayesha Asloob and Shikama, Akihiro (2017) Isotonian algebras. Nagoya Mathematical Journal . ISSN 0027-7630 (Print) 2152-6842 (Online) Published Online First http://dx.doi.org/10.1017/nmj.2017.4
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Official URL: http://dx.doi.org/10.1017/nmj.2017.4
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 Gro ̈bner basis.
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