AUTOMORPHISMS OF GLn ( R ) , R A LOCAL RING
نویسنده
چکیده
Let R denote a commutative local ring with maximal ideal m and residue field k — R/m. In this paper we determine the group automorphisms of the general linear group GL (R) when n > 3 and the characteristic of k is not 2.
منابع مشابه
AUTOMORPHISMS OF GLn ( R ) BY BERNARD
Let R be a commutative ring and S a multiplicatively closed subset of R having no zero divisors. The pair (.R, S) is said to be stable if the ring of fractions of R, S R, defined by S is a ring for which all finitely generated projective modules are free. For a stable pair (R, S) assume 2 is a unit in R and V is a free R-module of dimension > 3. This paper examines the action of a group automor...
متن کاملANNIHILATOR OF LOCAL COHOMOLOGY MODULES UNDER THE RING EXTENSION R⊂R[X]
Let R be a commutative Noetherian ring, I an ideal of R and M a non-zero R-module. In this paper we calculate the extension of annihilator of local cohomology modules H^t_I(M), t≥0, under the ring extension R⊂R[X] (resp. R⊂R[[X]]). By using this extension we will present some of the faithfulness conditions of local cohomology modules, and show that if the Lynch's conjecture, i...
متن کاملOn generalized left (alpha, beta)-derivations in rings
Let $R$ be a 2-torsion free ring and $U$ be a square closed Lie ideal of $R$. Suppose that $alpha, beta$ are automorphisms of $R$. An additive mapping $delta: R longrightarrow R$ is said to be a Jordan left $(alpha,beta)$-derivation of $R$ if $delta(x^2)=alpha(x)delta(x)+beta(x)delta(x)$ holds for all $xin R$. In this paper it is established that if $R$ admits an additive mapping $G : Rlongrigh...
متن کاملLocal Cohomology with Respect to a Cohomologically Complete Intersection Pair of Ideals
Let $(R,fm,k)$ be a local Gorenstein ring of dimension $n$. Let $H_{I,J}^i(R)$ be the local cohomology with respect to a pair of ideals $I,J$ and $c$ be the $inf{i|H_{I,J}^i(R)neq0}$. A pair of ideals $I, J$ is called cohomologically complete intersection if $H_{I,J}^i(R)=0$ for all $ineq c$. It is shown that, when $H_{I,J}^i(R)=0$ for all $ineq c$, (i) a minimal injective resolution of $H_{I,...
متن کامل" Multiplicative Invariant Theory " by Martin Lorenz
Let K be a commutative integral domain and let S = K[x1, x2, . . . , xn] denote the polynomial ring over K in the n variables x1, x2, . . . , xn. If H is a group of automorphisms of the free K-module V = Kx1 +Kx2 + · · ·+Kxn, that is, if H is a subgroup of GL(V ) ∼= GLn(K), then the linear action of H on V extends uniquely to a K-algebra action on S. The relationship between S, H, the H-stable ...
متن کامل