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1.
Let
be an algebraic algebra over an infinite field K and let
(
) be its group of units. We prove a stronger version of Hartley's conjecture for
, namely, if a Laurent polynomial identity (LPI, for short) f = 0 is satisfied in
(
), then
satisfies a polynomial identity (PI). We also show that if
is non-commutative, then
is a PI-ring, provided f = 0 is satisfied by the non-central units of
. In particular,
is locally finite and, thus, the Kurosh problem has a positive answer for K-algebras whose unit group is LPI. Moreover, f = 0 holds in
(
) if and only if the same identity is satisfied in
. The last fact remains true for generalized Laurent polynomial identities, provided that
is locally finite. 相似文献
2.
In 1929, Birkhoff proved the existence of an entire function F on
with the property that for any entire function f there exists a sequence {ak} of complex numbers such that {F(ζ+ak)} converges to f (ζ) uniformly on compact sets. Luh proved a variant of Birkhoff's theorem and the second author proved a theorem analogous to that of Luh for the multiplicative group
*. In this paper extensions of the above results to the multi-dimensional case are proved. Let M(n,
) be the set of all square matrices of degree n with complex coefficients, and let G=GL(n,
) be the general linear group of degree n over
. We denote by
(G) the set of all holomorphic functions on G. Similarly, we define
(
). Let K be the
(G)-hull of a compact set K in G. Finally we denote by B(G) the set of all compact subsets K of G with K=K such that there exists a holomorphic function f on M(n,
) with f(0)(f(K)), where (f(K)) is the
(
)-hull of f(K). Our main result is the following. There exists a holomorphic function F on G such that for any KB(G), for any function f holomorphic in some neighbourhood of K, and for any >0, there exists CG with maxZK |F(CZ)−f(Z)|<. 相似文献
3.
Pu Zhang 《Journal of Algebra》2002,250(2):709
Generalized Green classes are introduced; some basic properties of members in a generalized Green class are studied. Finally, we apply the results to
(Λ), the Ringel–Hall algebra of a finite-dimensional hereditary algebra Λ over a finite field. In particular, it is proved that
(Λ) belongs to a suitable generalized Green class, and that there is direct decomposition of spaces
(Λ) =
(Λ) J, where
(Λ) is the composition algebra of Λ and J is a twisted Hopf ideal of
(Λ), which is exactly the orthogonal complement of
(Λ). 相似文献
4.
Given a subset E of convex functions from
into
which satisfy growth conditions of order p>1 and an open bounded subset
of
, we establish the continuity of a map μΦμ from the set of all Young measures on
equipped with the narrow topology into a set of suitable functionals defined in
and equipped with the topology of Γ-convergence. Some applications are given in the setting of periodic and stochastic homogenization. 相似文献
5.
Paul Levy 《Journal of Algebra》2002,250(2):473
Let K be an algebraically closed field of positive characteristic and let G be a reductive group over K with Lie algebra
. This paper will show that under certain mild assumptions on G, the commuting variety
(
) is an irreducible algebraic variety. 相似文献
6.
Larry Smith 《Finite Fields and Their Applications》2002,8(4):504
Let
q be the finite field with q elements, q=pν, p
a prime, and Mat2.2(
q) the vector space of 2×2-matrices over
. The group GL(2,
) acts on Mat2,2(
q) by conjugation. In this note, we determine the invariants of this action. In contrast to the case of an infinite field, where the trace and determinant generate the ring of invariants, several new invariants appear in the case of finite fields. 相似文献
7.
A. Bir 《Indagationes Mathematicae》2000,11(4):499
Let z1, z2, …, zn be complex numbers, and write
for their power sums. Let
where the minimum is taken under the condition that
. In this paper we prove that
. 相似文献
8.
The following reaction-diffusion system in spatially non-homogeneous almost-periodic media is considered in a bounded domain
: (1) ∂tu=Au−f(u)+g, u|∂Ω=0. Here u=(u1,…,uk) is an unknown vector-valued function, f is a given nonlinear interaction function and the second order elliptic operator A has the following structure: where aijl(y) are given almost-periodic functions. We prove that, under natural assumptions on the nonlinear term f(u), the longtime behavior of solutions of (1) can be described in terms of the global attractor
of the associated dynamical system and that the attractors
, 0<<01, converge to the attractor
of the homogenized problem (1) as →0. Moreover, in the particular case of periodic media, we give explicit estimates for the distance between the non-homogenized
and the homogenized
attractors in terms of the parameter . 相似文献
9.
Julien Bichon 《Journal of Algebra》2000,230(2):83
Let
be a (small) category and let F:
→
algf be a functor, where
algf is the category of finite-dimensional measured algebras over a field k (or Frobenius algebras). We construct a universal Hopf algebra Aaut(F) such that F factorizes through a functor
:
→
coalgf(Aaut(F)), where
coalgf(Aaut(F)) is the category of finite-dimensional measured Aaut(F)-comodule algebras. This general reconstruction result allows us to recapture a finite-dimensional Hopf algebra A from the category
coalgf(A) and the forgetful functor ω:
coalgf(A) →
algf: we have A Aaut(ω). Our universal construction is also done in a C*-algebra framework, and we get compact quantum groups in the sense of Woronowicz. 相似文献
10.
Let C
n and C
n be the varieties of all completely regular and of all completely simple semigroups, respectively, whose idempotent generated subsemigroups are periodic with period n. We use Ol'shanski
's theory of geometric group presentations to show that for large odd n these varieties (and similarly defined varieties of epigroups) do not have finitely axiomatizable equational theories. 相似文献