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Nagoya Mathematical Journal Nagoya Mathematical Journal

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ISOTONIAN ALGEBRAS

Part of: Computational aspects and applications Ordered sets Theory of modules and ideals Algebraic combinatorics

Published online by Cambridge University Press:  08 March 2017

MINA BIGDELI ,
JÜRGEN HERZOG ,
TAKAYUKI HIBI ,
AYESHA ASLOOB QURESHI  and
AKIHIRO SHIKAMA
MINA BIGDELI
Affiliation:
Department of Mathematics, Institute for Advanced Studies in Basic Sciences (IASBS), Zanjan 45195-1159, Iran email mina.bigdeli@yahoo.com
JÜRGEN HERZOG
Affiliation:
Fachbereich Mathematik, Universität Duisburg-Essen, Fakultät für Mathematik, Essen 45117, Germany email juergen.herzog@uni-essen.de
TAKAYUKI HIBI
Affiliation:
Department of Pure and Applied Mathematics, Graduate School of Information Science and Technology, Osaka University, Suita, Osaka 565-0871, Japan email hibi@math.sci.osaka-u.ac.jp
AYESHA ASLOOB QURESHI
Affiliation:
SabancıUniversity, Orta Mahalle, Tuzla 34956, Istanbul, Turkey email aqureshi@sabanciuniv.edu
AKIHIRO SHIKAMA
Affiliation:
Department of Pure and Applied Mathematics, Graduate School of Information Science and Technology, Osaka University, Suita, Osaka 565-0871, Japan email a-shikama@cr.math.sci.osaka-u.ac.jp
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Abstract

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.

MSC classification

Primary: 13P10: Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases) 05E40: Combinatorial aspects of commutative algebra 13C99: None of the above, but in this section 06A11: Algebraic aspects of posets
Type
Article
Information
Nagoya Mathematical Journal , Volume 230 , June 2018 , pp. 83 - 101
Copyright
© 2017 by The Editorial Board of the Nagoya Mathematical Journal  

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