On the Cohen–Macaulay Property of Modular Invariant Rings
نویسندگان
چکیده
منابع مشابه
The Cohen - Macaulay Property of Invariant Rings
If V is a faithful module for a nite group G over a eld of characteristic p > 0, then the ring of invariants need not be Cohen-Macaulay if p divides the order of G. In this article the cohomology of G is used to study the question of Cohen-Macaulayness of the invariant ring. Let R = S(V) be the polynomial ring on which G acts. Then the main result can be stated as follow: If H r (G; R) 6 = 0 fo...
متن کاملSets of Non - Modular Invariant Rings
It is a classical problem to compute a minimal set of invariant polynomials generating the invariant ring of a finite group as an algebra. We present here an algorithm for the computation of minimal generating sets in the non-modular case. Apart from very few explicit computations of Gröbner bases, the algorithm only involves very basic operations, and is thus rather fast. As a test bed for com...
متن کاملOn Generators of Modular Invariant Rings of Finite Groups
Let G be a finite group, let V be an FG-module of finite dimension d, and denote by β(V ,G) the minimal number m such that the invariant ring S(V ) is generated by finitely many elements of degree at most m. A classical result of E. Noether says that β(V ,G) 6 |G| provided that charF is coprime to |G|!. If charF divides |G|, then no bounds for β(V ,G) are known except for very special choices o...
متن کاملOn Generators of Modular Invariant Rings of Nite Groups
Let G be a nite group, let V be an F G-module of nite dimension d, and denote by (V; G) the minimal number m such that the invariant ring S(V) G is generated by nitely many elements of degree at most m. A classical result of E. Noether says that (V; G) jGj provided that char F is coprime to jGj!. If char F divides jGj then no bounds for (V; G) are known except for very special choices of G. In ...
متن کاملOn the Intersection of Invariant Rings
Based on Weitzenböck’s theorem and Nagata’s counterexample for Hilbert’s fourteenth problem we construct two finitely generated invariant rings R,S ⊂ K[x1, x2, . . . , xn] s.t. the intersection R ∩ S is not finitely generated as a K-algebra.
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ژورنال
عنوان ژورنال: Journal of Algebra
سال: 1999
ISSN: 0021-8693
DOI: 10.1006/jabr.1998.7716