共查询到20条相似文献,搜索用时 15 毫秒
1.
2.
LetD be a division ring with a centerC, andD[X
1, …,X
N] the ring of polynomials inN commutative indeterminates overD. The maximum numberN for which this ring of polynomials is primitive is equal to the maximal transcendence degree overC of the commutative subfields of the matrix ringsM
n(D),n=1, 2, …. The ring of fractions of the Weyl algebras are examples where this numberN is finite. A tool in the proof is a non-commutative version of one of the forms of the “Nullstellensatz”, namely, simpleD[X
1, …,X
m]-modules are finite-dimensionalD-spaces.
This paper was written while the authors were Fellows of the Institute for Advanced Studies, The Hebrew University of Jerusalem,
Mount Scopus, Jerusalem, Israel. 相似文献
3.
4.
5.
Two square matrices A and B over a ring R are semisimilar, written AB, if YAX=B and XBY=A for some (possibly rectangular) matrices X, Y over R. We show that if A and B have the same dimension, and if the ring is a division ring , then AB if and only if A2 is similar to B2 and rank(Ak)=rank(Bk), k=1,2,… 相似文献
6.
On polynomial rings over a ring with a selfduality 总被引:2,自引:0,他引:2
Zhang Shenggui 《数学学报(英文版)》1997,13(4):571-576
We prove that a ringR has a self duality induced by a leftR-moduleM if and only if its polynomial ringR[x] has a graded self duality induced by a graded leftR[x]-moduleM[x
−1].
Supported by the Natural Science Foundation of Fujian Province (1994–1997) 相似文献
7.
Martin Schwachhöfer 《Semigroup Forum》1996,53(1):330-345
Given an-dimensional right vector spaceV over a division ring
we denote byS the semigroup of the endomorphisms ofV and designate this semigroup as alinear semigroup. First we prove that every automorphism ofS can be written asT→fTf
−1, wheref∶V→V is a semilinear homeomorphism. Furthermore, we show that every isomorphism between maximal compact subsemigroups ofS is also of this type. 相似文献
8.
Peter Šemrl 《Israel Journal of Mathematics》2008,163(1):125-138
Let
be an arbitrary division ring and M
n
(
) the multiplicative semigroup of all n × n matrices over
. We describe the general form of endomorphisms of M
n
(
).
Supported in part by a grant from the Ministry of Science of Slovenia. 相似文献
9.
Sergei Evdokimov 《Journal of Combinatorial Theory, Series A》2010,117(7):827-841
It is proved that any Schur ring over a Galois ring of odd characteristic is either normal, or of rank 2, or a non-trivial generalized wreath product. The normal Schur rings are characterized as a special subclass of the cyclotomic Schur rings. 相似文献
10.
11.
12.
A Wedderburn polynomial over a division ring K is a minimal polynomial of an algebraic subset of K. Such a polynomial is always a product of linear factors over K, although not every product of linear polynomials is a Wedderburn polynomial. In this paper, we establish various properties and characterizations of Wedderburn polynomials over K, and show that these polynomials form a complete modular lattice that is dual to the lattice of full algebraic subsets of K. Throughout the paper, we work in the general setting of an Ore skew polynomial ring K[t,S,D], where S is an endomorphism of K and D is an S-derivation on K. 相似文献
13.
Esther Beneish 《Transactions of the American Mathematical Society》2004,356(4):1609-1622
Let be a finite group, let be a -lattice, and let be a field of characteristic zero containing primitive roots of 1. Let be the quotient field of the group algebra of the abelian group . It is well known that if is quasi-permutation and -faithful, then is stably equivalent to . Let be the center of the division ring of generic matrices over . Let be the symmetric group on symbols. Let be a prime. We show that there exist a split group extension of by a -elementary group, a -faithful quasi-permutation -lattice , and a one-cocycle in such that is stably isomorphic to . This represents a reduction of the problem since we have a quasi-permutation action; however, the twist introduces a new level of complexity. The second result, which is a consequence of the first, is that, if is algebraically closed, there is a group extension of by an abelian -group such that is stably equivalent to the invariants of the Noether setting .
14.
We analyze some commutation properties of the sets of mappings of a vector space X over a division ring K with a conjugation j which are relevant when studying symmetries in quantum mechanics and in elementary-particle physics. The first part of the paper is devoted to the “linear-antilinear centralizer” c, i.e. to the group of the linear and antilinear (j-semilinear) invertible mappings which commute with a given set of mappings of X. Some nontrivial results which connect properties of with properties of c are obtained, and a classification of the sets of mappings of X is found by means of purely algebraic techniques. This classification is more detailed than that usually adopted by physicists. The second part of the paper is devoted to the ?-linear commutant ′λ, i.e. to the set of mappings of X which commute with and which are linear with respect to the j-invariant subring ? of K. We investigate the structure of ′λ in connection with the structure and some of the properties of . In the third part, we show how the results obtained in the preceding sections simplify when the division ring K is of type II (according to a classification introduced in an earlier work). Finally, we illustrate with simple examples in one- and two-dimensional vector spaces all the cases which can occur. 相似文献
15.
Let Ks(R) be the generalized matrix ring over a ring R with multiplier s. For a general local ring R and a central element s in the Jacobson radical of R, necessary and sufficient conditions are obtained for Ks(R) to be a strongly clean ring. For a commutative local ring R and an arbitrary element s in R, criteria are obtained for a single element of Ks(R) to be strongly clean and, respectively, for the ring Ks(R) to be strongly clean. Specializing to s = 1 yields some known results. New families of strongly clean rings are presented. 相似文献
16.
The subgroups, full of transvections, of unitary groups over division rings with an involution are described.
Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR,
Vol. 160, pp. 193–200, 1987. 相似文献
17.
Andrzej Sladek 《代数通讯》2013,41(7):2159-2175
We study basic properties of Auslander-Gorenstein rings related to duality, localization and purity of minimal injective resolutions. 相似文献
18.
19.
20.