On the relations of isotonian algebras
Authors:
Jürgen Herzog, Ayesha Asloob Qureshi and Akihiro Shikama
Journal:
Proc. Amer. Math. Soc. 145 (2017), 4119-4126
MSC (2010):
Primary 05E45, 05E40, 13C99
DOI:
https://doi.org/10.1090/proc/13502
Published electronically:
June 9, 2017
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Abstract | References | Similar Articles | Additional Information
Abstract: It is shown that for large classes of posets 
and 
, the defining ideal 
of an isotonian algebra is generated by squarefree binomials. Within these classes, those posets are classified for which 
is quadratically generated.
- [1] M. Bigdeli, J. Herzog, T. Hibi, A. Shikama, and A. A. Qureshi, Isotonian algebras, arXiv:1512.01973
- [2] G. Fløystad, B. M. Greve, and J. Herzog, Letterplace and co-letterplace ideals of posets.
- [3] Viviana Ene, Jürgen Herzog, and Fatemeh Mohammadi, Monomial ideals and toric rings of Hibi type arising from a finite poset, European J. Combin. 32 (2011), no. 3, 404-421. MR 2764804, https://doi.org/10.1016/j.ejc.2010.11.006
- [4] Jürgen Herzog and Takayuki Hibi, Monomial ideals, Graduate Texts in Mathematics, vol. 260, Springer-Verlag London, Ltd., London, 2011. MR 2724673
- [5] Jürgen Herzog, Ayesha Asloob Qureshi, and Akihiro Shikama, Alexander duality for monomial ideals associated with isotone maps between posets, J. Algebra Appl. 15 (2016), no. 5, 1650089, 6. MR 3479448, https://doi.org/10.1142/S0219498816500894
- [6] Takayuki Hibi, Distributive lattices, affine semigroup rings and algebras with straightening laws, Commutative algebra and combinatorics (Kyoto, 1985) Adv. Stud. Pure Math., vol. 11, North-Holland, Amsterdam, 1987, pp. 93-109. MR 951198
- [7] Viviana Ene, Jürgen Herzog, and Sara Saeedi Madani, A note on the regularity of Hibi rings, Manuscripta Math. 148 (2015), no. 3-4, 501-506. MR 3414489, https://doi.org/10.1007/s00229-015-0752-8
- [8] Martina Juhnke-Kubitzke, Lukas Katthän, and Sara Saeedi Madani, Algebraic properties of ideals of poset homomorphisms, J. Algebraic Combin. 44 (2016), no. 3, 757-784. MR 3552906, https://doi.org/10.1007/s10801-016-0687-5
- [9] G. Fløystad and A. Nematbakhsh, Rigid ideals by deforming quadratic letterplace ideals.
- [10] A. D'Alí, G. Fløystad, and A. Nematbakhsh, Resolutions of co-letterplace ideals and generalizations of Bier spheres. arXiv:1601.02793
- [11] A. D'Alí, G. Fløystad, and A. Nematbakhsh, Resolutions of letterplace ideals of posets. J. Algebr. Comb. (2016). doi:10.1007/s10801-016-0729-z
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Additional Information
Jürgen Herzog
Affiliation:
Fakultät für Mathematik, Fachbereich Mathematik, Universität Duisburg-Essen, 45117 Essen, Germany
Email:
juergen.herzog@uni-essen.de
Ayesha Asloob Qureshi
Affiliation:
Faculty of Engineering and Natural Sciences, Sabancı University, 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, Toyonaka, Osaka 560-0043, Japan
Email:
a-shikama@cr.math.sci.osaka-u.ac.jp
DOI:
https://doi.org/10.1090/proc/13502
Received by editor(s):
September 6, 2016
Published electronically:
June 9, 2017
Additional Notes:
This paper was partially written during the stay of the second author at The Abdus Salam International Centre of Theoretical Physics (ICTP), Trieste, Italy
Communicated by:
Irena Peeva
Article copyright:
© Copyright 2017
American Mathematical Society
