共查询到20条相似文献,搜索用时 31 毫秒
1.
David R. Finston 《代数通讯》2013,41(7):1597-1626
In [5] it was shown that for a polynomial P of precise degree n with coefficients in an arbitrary m-ary algebra of dimension d as a vector space over an algebraically closed fields, the zeros of P together with the homogeneous zeros of the dominant part of P form a set of cardinality nd or the cardinality of the base field. We investigate polynomials with coefficients in a d dimensional algebra A without assuming the base field k to be algebraically closed. Separable polynomials are defined to be those which have exactly nd distinct zeros in [Ktilde] ?k A [Ktilde] where [Ktilde] denotes an algebraic closure of k. The main result states that given a separable polynomial of degree n, the field extension L of minimal degree over k for which L ?k A contains all nd zeros is finite Galois over k. It is shown that there is a non empty Zariski open subset in the affine space of all d-dimensional k algebras whose elements A have the following property: In the affine space of polynomials of precise degree n with coefficients in A there is a non empty Zariski open subset consisting of separable polynomials; in other polynomials with coefficients in a finite dimensional algebra are “generically” separable. 相似文献
2.
B. Weisfeiler 《Journal of Algebra》1979,60(2):485-519
Abstract homomorphisms with Zariski-dense image of the group of rational points of anisotropic almost simple algebraic groups over real closed fields into other almost simple algebraic groups are described. The result states, in particular, that the kernel of such homomorphism is a congruence subgroup of the original group. 相似文献
3.
Markus Junker 《Israel Journal of Mathematics》1999,109(1):273-298
Zariski groups are ℵ0-stable groups with an axiomatically given Zariski topology and thus abstract generalizations of algebraic groups. A large
part of algebraic geometry can be developed for Zariski groups. As a main result, any simple smooth Zariski group interprets
an algebraically closed field, hence is almost an algebraic group over an algebraically closed field. 相似文献
4.
Zha Jianguo 《数学年刊B辑(英文版)》1997,18(2):167-172
HOMOMORPHISMSBETWEENCHEVALLEYGROUPSOFTYPESCnANDG2OVERFINITEFIELDSZHAJIANGUOManuscriptreceivedNovember2,1994.DepartmentofApp... 相似文献
5.
Françoise Reynaud 《Discrete Mathematics》1975,12(1):37-53
The paper deals with tournaments (i.e., with trichotomic relations) and their homomorphisms. The study of tournaments by means of their homomorphisms is natural as tournaments are algebras of a special kind. We prove (1) theorems which relate combinatorial and algebraic notions (e.g., the score of a tournament and the monoid of its endomorphisms); (2) theorems concerned with strictly algebraic aspects of tournaments (e.g., characterizing the lattice of congruences of a tournament). Our main result is that the group of automorphisms and the lattice of congruences of a tournament are in general independent. In the last part of the paper we give some examples and applications to other fields. 相似文献
6.
Dipendra Prasad 《Compositio Mathematica》1999,119(3):343-354
Let K be a quadratic extension of a field k which is either local field or a finite field. Let G be an algebraic group over k. The aim of the present paper is to understand when a representation of G(K) has a G(k) invariant linear form. We are able to accomplish this in the case when G is the group of invertible elements of a division algebra over k of odd index if k is a local field, and for general connected groups over finite fields. 相似文献
7.
8.
设F,K为域,GLn(F),SLn(F)分别表示F上的n级一般线生群和n级特殊线性群.PGLn(F),PSLn(F)分别表示F上的n级射影一般线性群和n级射影特殊线性群.φ:SLn(F)→PGLn(K),n≥3为非平凡同态.本文确定了当K的持征为2时η的—个性质. 相似文献
9.
We prove that every mapping torus of any free group endomorphism is residually finite. We show how to use a not yet published result of E. Hrushovski to extend our result to arbitrary linear groups. The proof uses algebraic self-maps of affine spaces over finite fields. In particular, we prove that when such a map is dominant, the set of its fixed closed scheme points is Zariski dense in the affine space. 相似文献
10.
Emmanuel Breuillard Ben Green Robert Guralnick Terence Tao 《Israel Journal of Mathematics》2012,192(1):347-379
We show that (with one possible exception) there exist strongly dense free subgroups in any semisimple algebraic group over a large enough field. These are nonabelian free subgroups all of whose subgroups are either cyclic or Zariski dense. As a consequence, we get new generating results for finite simple groups of Lie type and a strengthening of a theorem of Borel related to the Hausdorff-Banach-Tarski paradox. In a sequel to this paper, we use this result to also establish uniform expansion properties for random Cayley graphs over finite simple groups of Lie type 相似文献
11.
Chow’s Theorem for Semi-abelian Varieties and Bounds for Splitting Fields of Algebraic Tori 下载免费PDF全文
A theorem of Chow concerns homomorphisms of two abelian varieties under a primary field extension base change. In this paper, we generalize Chow's theorem to semi-abelian varieties. This contributes to different proofs of a well-known result that every algebraic torus splits over a finite separable field extension. We also obtain the best bound for the degrees of splitting fields of tori. 相似文献
12.
Mariusz Budziński 《代数通讯》2017,45(4):1627-1638
The notion of a quantum family of maps has been introduced in the framework of C*-algebras. As in the classical case, one may consider a quantum family of maps preserving additional structures (e.g. quantum family of maps preserving a state). In this paper, we define a quantum family of homomorphisms of locally compact quantum groups. Roughly speaking, we show that such a family is classical. The purely algebraic counterpart of the discussed notion, i.e. a quantum family of homomorphisms of Hopf algebras, is introduced and the algebraic counterpart of the aforementioned result is proved. Moreover, we show that a quantum family of homomorphisms of Hopf algebras is consistent with the counits and coinverses of the given Hopf algebras. We compare our concept with weak coactions introduced by Andruskiewitsch and we apply it to the analysis of adjoint coaction. 相似文献
13.
In this paper we bring together results about the density of subsemigroups of abelian Lie groups, the minimal number of topological generators of abelian Lie groups and a result about actions of algebraic groups. We find the minimal number of generators of a finitely generated abelian semigroup or group of matrices with a dense or a somewhere dense orbit by computing the minimal number of generators of a dense subsemigroup (or subgroup) of the connected component of the identity of its Zariski closure. 相似文献
14.
Enrique Artal Bartolo Jorge Carmona Ruber José Ignacio Cogolludo Agustí n 《Transactions of the American Mathematical Society》2007,359(1):165-183
In this paper we construct new invariants of algebraic curves based on (not necessarily generic) braid monodromies. Such invariants are effective in the sense that their computation allows for the study of Zariski pairs of plane curves. Moreover, the Zariski pairs found in this work correspond to curves having conjugate equations in a number field, and hence are not distinguishable by means of computing algebraic coverings. We prove that the embeddings of the curves in the plane are not homeomorphic. We also apply these results to the classification problem of elliptic surfaces.
15.
Jrg Winkelmann 《Mathematische Nachrichten》1997,186(1):285-302
We investigate under which conditions an algebraic group G defined over a locally compact field k admitr a subgroup Γ? G(k) which is dense in the Zariski topology, but discerte in the topology induced by the locally compact topology on k. For non—solvable groups we provide a complete answer. 相似文献
16.
This paper dualizes the setting of affine spaces as originally introduced by Diers for application to algebraic geometry and expanded upon by various authors, to show that the fundamental groups of pointed topological spaces appear as the structures of dually affine spaces. The dual of the Zariski closure operator is introduced, and the 1-sphere and its copowers together with their fundamental groups are shown to be examples of complete objects with respect to the Zariski dual closure operator. 相似文献
17.
Franz-Viktor Kuhlmann 《Advances in Mathematics》2004,188(2):399-424
We consider the Zariski space of all places of an algebraic function field F|K of arbitrary characteristic and investigate its structure by means of its patch topology. We show that certain sets of places with nice properties (e.g., prime divisors, places of maximal rank, zero-dimensional discrete places) lie dense in this topology. Further, we give several equivalent characterizations of fields that are large, in the sense of F. Pop's Annals paper Embedding problems over large fields. We also study the question whether a field K is existentially closed in an extension field L if L admits a K-rational place. In the appendix, we prove the fact that the Zariski space with the Zariski topology is quasi-compact and that it is a spectral space. 相似文献
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19.
Maria Manuel Clementino Dirk Hofmann George Janelidze 《Applied Categorical Structures》2016,24(5):733-742
We study exponentiability of homomorphisms in varieties of universal algebras close to classical ones. After describing an “almost folklore” general result, we present a purely algebraic proof of “étale implies exponentiable”, alternative to the topologically motivated proof given in one of our previous papers, in a different context. We prove that only isomorphisms are exponentiable homomorphisms in ideal determined varieties and extend this to ideal determined categories. Finally, we give a complete characterization of exponentiable homomorphisms of semimodules over semirings. 相似文献
20.
R. Pink 《Commentarii Mathematici Helvetici》2000,75(4):608-643
Consider a finitely generated Zariski dense subgroup of a connected simple algebraic group G over a global field F. An important aspect of strong approximation is the question of whether the closure of in the group of points of G with coefficients in a ring of partial adeles is open. We prove an essentially optimal result in this direction, based on
the condition that is not discrete in that ambient group. There are no restrictions on the characteristic of F or the type of G, and simultaneous approximation in finitely many algebraic groups is also studied. Classification of finite simple groups
is not used.
Received: August 31, 1999. 相似文献