Monomial Difference Ideals

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. Moreover, the Alexander Duality for monomial ideals is generalized to the monomial case.

arXiv comment16 pages

References in corpus (1)

• Binomial Difference Ideal and Toric Difference Variety

Cited by in corpus (2)

• Criteria for Finite Difference Groebner Bases of Normal Binomial Difference Ideals
• Finite Basis for Radical Well-Mixed Difference Ideals Generated by Binomials