共查询到20条相似文献,搜索用时 15 毫秒
1.
P. S. Kolesnikov 《Algebra and Logic》2001,40(4):219-230
We consider an algebraically closed (in the sense of solvability of arbitrary polynomial equations) skew field constructed by Makar-Limanov. It is shown that every generalized polynomial equation with more than one homogeneous component has a non-zero solution. We also look into P. Cohn's approach to defining algebraically closed non-commutative skew fields and treat some related problems. 相似文献
2.
3.
YU XiaoLan & LU DiMing 《中国科学 数学(英文版)》2011,(7)
Let G be a finite group and A be a finite-dimensional selfinjective algebra over an algebraically closed field. Suppose A is a left G-module algebra. Some suficient conditions for the skew group algebra AG to be stably Calabi-Yau are provided, and some new examples of stably Calabi-Yau algebras are given as well. 相似文献
4.
Yu. L. Ershov 《Algebra and Logic》2004,43(5):327-330
It is shown that every finite-dimensional skew field whose center is an extremal valued field is defect free. We construct an example of an algebraically complete valued field such that a finite-dimensional skew field over it has a non-trivial defect, that is, there exist algebraically complete valued fields that are not extremal. 相似文献
5.
Sourav Sen 《Archiv der Mathematik》2020,114(4):377-381
During recent decades, $$\mathbb {G}_a$$-actions, especially certain invariants of $$\mathbb {G}_a$$-actions, have been important tools in the study of affine varieties. The $$\mathbb {G}_a$$-actions are usually studied through locally nilpotent derivations in characteristic zero and exponential maps (see Definition 1.1) in arbitrary characteristic. The “Makar-Limanov invariant” of locally nilpotent derivations played a pivotal role in solving the linearization conjecture in the 1990s, while invariants of exponential maps were central to N. Gupta’s resolution of the Zariski cancellation problem in positive characteristic. In the study of locally nilpotent derivations on commutative algebras containing $$\mathbb {Q}$$, Freudenburg and Moser-Jauslin (Mich Math J 62:227–258, (2013), Theorem 6.1) have introduced a new invariant called “rigid core” and used it to formulate an alternative version of Mason’s theorem and to prove a well-known analogue of Fermat’s last theorem for rational functions (Freudenburg and Moser-Jauslin (2013), Corollary 6.1). In this note, we consider the concept of the rigid core in the framework of exponential maps on commutative algebras over an algebraically closed field k of arbitrary characteristic. We observe that for any factorial k-domain B with $${\text {tr.deg}}_k(B)=2$$, the concept of rigid core coincides with the Makar-Limanov invariant. We also show that over any affine two-dimensional normal k-domain B, its rigid core is a stable invariant. 相似文献
6.
Kirby C. Smith 《代数通讯》2013,41(4):331-346
Let R be a noncommutative polynomial ring over the division ring K where K has center F. Then R = K[x,σ,D]where σ is a monomorphism of K and D is a σ-derivaton K. R is called dimension finite if (K: Fσ)<∞ and (K: FD)<∞ where Fσ is the subfield of F fixed under σand FD is the subfied of F of D-constants. R is algebraically closed if every nonconstant polynomial in Rfactors completely into linear factors. The algebraically closed dimension finite polynomial rings are determined. s done by reducing the problem to two classes: skew polynomial rings and differential polynomial rings. Examples algebraically closed polynomial rings which are not dimensfinite are given. 相似文献
7.
Let H be a Hopf algebra with a finite-dimensional, nontrivial space of skew primitive elements, over an algebraically closed field of characteristic zero. We prove that H contains either the polynomial algebra as a Hopf subalgebra, or a certain Schurian simple-pointed Hopf subalgebra. As a consequence, a complete list of the locally finite, simple-pointed Hopf algebras is obtained. Also, the graded automorphism group of a Hopf algebra on a Schurian Hopf quiver is determined, and the relation between this group and the automorphism groups of the corresponding Hopf quiver, is clarified. 相似文献
8.
《Annals of Pure and Applied Logic》2020,171(9):102822
In this paper we extend of the notion of algebraically closed given in the case of groups and skew fields to an arbitrary h-inductive theory. The main subject of this paper is the study of the notion of positive algebraic closedness and its relationship with the notion of positive closedness and the amalgamation property. 相似文献
9.
Julie Dionne 《Journal of Pure and Applied Algebra》2009,213(2):241-228
We show that the main results of Happel-Rickard-Schofield (1988) and Happel-Reiten-Smalø (1996) on piecewise hereditary algebras are coherent with the notion of group action on an algebra. Then, we take advantage of this compatibility and show that if G is a finite group acting on a piecewise hereditary algebra A over an algebraically closed field whose characteristic does not divide the order of G, then the resulting skew group algebra A[G] is also piecewise hereditary. 相似文献
10.
Manish Kumar 《Journal of Algebra》2008,319(12):5178-5207
11.
Vladimir V. Sergeichuk 《Linear algebra and its applications》2008,428(1):154-192
We give canonical matrices of a pair (A,B) consisting of a nondegenerate form B and a linear operator A satisfying B(Ax,Ay)=B(x,y) on a vector space over F in the following cases:
- •
- F is an algebraically closed field of characteristic different from 2 or a real closed field, and B is symmetric or skew-symmetric;
- •
- F is an algebraically closed field of characteristic 0 or the skew field of quaternions over a real closed field, and B is Hermitian or skew-Hermitian with respect to any nonidentity involution on F.
12.
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
13.
Ehud Hrushovski 《Israel Journal of Mathematics》1992,79(2-3):129-151
(1) We construct a strongly minimal expansion of an algebraically closed field of a given characteristic. Actually we show
a much more general result, implying for example the existence of a strongly minimal set with two different field structures
of distinct characteristics.
(2) A strongly minimal expansion of an algebraically closed field that preserves the algebraic closure relation must be an
expansion by (algebraic) constants.
Supported by NSF grants DMS 8903378. 相似文献
14.
Anquela José Angel 《代数通讯》2013,41(5):1409-1427
In this paper we prove that two finite-dimensional linear Jordan algebras over an algebraically closed field with isothermic lattices of subalgebras must bi isothemic if one of them is semisimple non-isothermic to F. As a corollary of this fact, we prove that two unital Jordan algebras with isothermic lattices of subalgebras must have the same dimension when the ground field is algebraically closed of characteristic zero. Through this work we see similar results in more general fields for particular families of simple Jordan algebras. 相似文献
15.
Under suitable hypotheses, we prove that a form of a projective homogeneous variety G/P defined over the function field of a surface over an algebraically closed field has a rational point. The method uses an
algebro-geometric analogue of simple connectedness replacing the unit interval by the projective line. As a consequence, we
complete the proof of Serre’s Conjecture II in Galois cohomology for function fields over an algebraically closed field. 相似文献
16.
E. I. hustin 《代数通讯》2013,41(3):1145-1163
Let K be an algebraically closed field of characteristic zero or a real closed field. We prove that over the field K every polynomial in one variable of degree mn is the resultant of two polynomials in two variables of degrees m and n 相似文献
17.
David R. Finston 《manuscripta mathematica》1987,58(1-2):229-244
In [5] it was shown that a finite dimensional binary algebra without nilpotents over an algebraically closed field of characteristic zero has only the trivial derivation and, consequently, a finite automorphism group. It is shown here that an m-ary algebra without nilpotents has only finitely many endomorphisms, with no assumptions on the characteristic of the base field. An upper bound on the dimension of the algebraic set of endomorphisms of a finite dimensional m-ary algebra, depending on the dimension of a maximal null subalgebra, is obtained if the base field is the complex field. The null subalgebras arising from a single derivation are examined for the case of an algebraically closed base field of characteristic zero. 相似文献
18.
N. V. Grigorehko 《Mathematical Notes》1975,17(1):66-68
A classification is given of Pcard-Vessiot extensions with an Abelian Galois group for a partial differential field of characteristic zero with an algebraically closed field of constants. 相似文献
19.
Let F be a field, G a finite group, H a normal subgroup of prime index p, and V an irreducible FH-module. If F is algebraically closed and of characteristic 0, the FG-module induced from V is either irreducible or a direct sum of p pairwise nonisomorphic irreducible modules. It is shown here that if F is not assumed algebraically closed and its characteristic is not 0, then there are not two but six possibilities for the structure of the induced module. 相似文献
20.
Christopher P. Bendel 《Proceedings of the American Mathematical Society》2001,129(3):671-676
In this paper, it is shown that the projectivity of a rational module for an infinitesimal unipotent group scheme over an algebraically closed field of positive characteristic can be detected on a family of closed subgroups. 相似文献