Automorphism-invariant non-singular rings and modules
نویسندگان
چکیده
منابع مشابه
Automorphism Groups of Non-singular Plane Curves of Degree 5
Let Mg be the moduli space of smooth, genus g curves over an algebraically closed field K of zero characteristic. Denote by Mg(G) the subset of Mg of curves δ such that G (as a finite non-trivial group) is isomorphic to a subgroup of Aut(δ) and let M̃g(G) be the subset of curves δ such that G ∼= Aut(δ) where Aut(δ) is the full automorphism group of δ. Now, for an integer d ≥ 4, let MPl g be the ...
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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...
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In 1993, Muzychuk [18] showed that the rational Schur rings over a cyclic group Zn are in one-to-one correspondence with sublattices of the divisor lattice of n, or equivalently, with sublattices of the lattice of subgroups of Zn. This can easily be extended to show that for any finite group G, sublattices of the lattice of characteristic subgroups of G give rise to rational Schur rings over G ...
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Proof. Consider the map g:A/I → C , a+I 7→ f (a). It is well defined: a+I = a′ +I implies a− a′ ∈ I implies f (a) = f (a′). The element a + I belongs to the kernel of g iff g(a + I) = f (a) = 0, i.e. a ∈ I , i.e. a + I = I is the zero element of A/I . Thus, ker(g) = 0. The image of g is g(A/I) = {f (a) : a ∈ A} = C . Thus, g is an isomorphism. The inverse morphism to g is given by f (a) 7→ a + I .
متن کاملGraded Rings and Modules
1 Definitions Definition 1. A graded ring is a ring S together with a set of subgroups Sd, d ≥ 0 such that S = ⊕ d≥0 Sd as an abelian group, and st ∈ Sd+e for all s ∈ Sd, t ∈ Se. One can prove that 1 ∈ S0 and if S is a domain then any unit of S also belongs to S0. A homogenous ideal of S is an ideal a with the property that for any f ∈ a we also have fd ∈ a for all d ≥ 0. A morphism of graded r...
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ژورنال
عنوان ژورنال: Journal of Algebra
سال: 2017
ISSN: 0021-8693
DOI: 10.1016/j.jalgebra.2017.05.013