Negative solutions to three-dimensional monomial Noether problem
نویسندگان
چکیده
منابع مشابه
Negative solutions to three-dimensional monomial Noether problem
Three-dimensional monomial Noether problem can have negative solutions for 8 groups by the suitable choice of the coefficients. We find the necessary and sufficient condition for the coefficients to have a negative solution. The results are obtained by two criteria of irrationality using Galois cohomology.
متن کاملNoether normalization guided by monomial cone decompositions
This paper explains the relevance of partitioning the set of standard monomials into cones for constructing a Noether normalization for an ideal in a polynomial ring. Such a decomposition of the complement of the corresponding initial ideal in the set of all monomials – also known as a Stanley decomposition – is constructed in the context of Janet bases, in order to come up with sparse coordina...
متن کاملRationality problem of three-dimensional purely monomial group actions: the last case
A k-automorphism σ of the rational function field k(x1, . . . , xn) is called purely monomial if σ sends every variable xi to a monic Laurent monomial in the variables x1, . . . , xn. Let G be a finite subgroup of purely monomial k-automorphisms of k(x1, . . . , xn). The rationality problem of the G-action is the problem of whether the G-fixed field k(x1, . . . , xn) G is k-rational, i.e., pure...
متن کاملPERIODIC SOLUTIONS OF CERTAIN THREE DIMENSIONAL AUTONOMOUS SYSTEMS
There has been extensive work on the existence of periodic solutions for nonlinear second order autonomous differantial equations, but little work regarding the third order problems. The popular Poincare-Bendixon theorem applies well to the former but not the latter (see [2] and [3]). We give a necessary condition for the existence of periodic solutions for the third order autonomous system...
متن کاملDeterminantal ideals and monomial curves in the three-dimensional space
We show that the defining ideal of every monomial curve in the affine or projective three-dimensional space can be set-theoretically defined by three binomial equations, two of which set-theoretically define a determinantal ideal generated by the 2-minors of a 2× 3 matrix with monomial entries.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Algebra
سال: 2012
ISSN: 0021-8693
DOI: 10.1016/j.jalgebra.2012.07.018