Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

Request Permissions   Purchase Content 
 

 

Monomial difference ideals


Author: Jie Wang
Journal: Proc. Amer. Math. Soc. 145 (2017), 1481-1496
MSC (2010): Primary 12H10
DOI: https://doi.org/10.1090/proc/13369
Published electronically: October 20, 2016
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: In this paper, basic properties of monomial difference ideals are studied. We prove the finitely generated property of well-mixed difference ideals generated by monomials. Furthermore, a finite prime decomposition of radical well-mixed monomial difference ideals is given. As a consequence, we prove that every strictly ascending chain of radical well-mixed monomial difference ideals in a difference polynomial ring is finite, which answers a question raised by E. Hrushovski in the monomial case.


References [Enhancements On Off] (What's this?)

  • [1] Jürgen Herzog and Takayuki Hibi, Monomial ideals, Graduate Texts in Mathematics, vol. 260, Springer-Verlag London, Ltd., London, 2011. MR 2724673
  • [2] E. Hrushovski, The elementary theory of the Frobenius automorphisms. Available from http://www.ma.huji.ac.il/˜ehud/, 2012.
  • [3] X. S. Gao, C. M. Yuan, and Z. Huang, Binomial difference ideal and toric difference variety, arXiv:1404.7580, 2015.
  • [4] Alexander Levin, On the ascending chain condition for mixed difference ideals, Int. Math. Res. Not. IMRN 10 (2015), 2830–2840. MR 3352257, https://doi.org/10.1093/imrn/rnu021
  • [5] Ezra Miller and Bernd Sturmfels, Combinatorial commutative algebra, Graduate Texts in Mathematics, vol. 227, Springer-Verlag, New York, 2005. MR 2110098
  • [6] Richard P. Stanley, The upper bound conjecture and Cohen-Macaulay rings, Studies in Appl. Math. 54 (1975), no. 2, 135–142. MR 0458437
  • [7] M. Wibmer, Algebraic difference equations, preprint, 2013.
  • [8] M. Wibmer, Affine difference algebraic groups, arXiv:1405.6603, 2014.

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2010): 12H10

Retrieve articles in all journals with MSC (2010): 12H10


Additional Information

Jie Wang
Affiliation: KLMM, Academy of Mathematics and Systems Science, The Chinese Academy of Sciences, Beijing 100190, People’s Republic of China
Email: wangjie212@mails.ucas.ac.cn

DOI: https://doi.org/10.1090/proc/13369
Keywords: Monomial difference ideal, well-mixed difference ideal, Hrushovski's question, decomposition of difference ideal
Received by editor(s): January 14, 2016
Received by editor(s) in revised form: June 16, 2016
Published electronically: October 20, 2016
Communicated by: Lev Borisov
Article copyright: © Copyright 2016 American Mathematical Society