共查询到20条相似文献,搜索用时 15 毫秒
1.
Glaz and Wickless introduced the class G of mixed abelian groups A which have finite torsion-free rank and satisfy the following three properties: i) A
p is finite for all primes p, ii) A is isomorphic to a pure subgroup of
P
A
P and iii) Hom(A, tA) is torsion. A ring R is a left Kasch ring if every proper right ideal of R has a non-zero left annihilator. We characterize the elements A of G such that E(A)/tE(A) is a left Kasch ring, and discuss related results. 相似文献
2.
Dikran Dikranjan 《代数通讯》2015,43(1):212-224
Using the nice properties of the w-divisible weight and the w-divisible groups, we prove a factorization theorem for compact abelian groups K; namely, K = K tor × K d , where K tor is a bounded torsion compact abelian group and K d is a w-divisible compact abelian group. By Pontryagin duality this result is equivalent to the same factorization for discrete abelian groups proved in [9]. 相似文献
3.
An abelian group A is an S-group (S +-group) if every subgroup B ≤ A of finite index is A-generated (A-solvable). This article discusses some of the differences between torsion-free S-groups and mixed S-groups, and studies (mixed) S- and S +-groups, which are self-small and have finite torsion-free rank. 相似文献
4.
G. M. Feldman 《Journal of Theoretical Probability》2004,17(4):929-941
It is well-known Heyde's characterization theorem for the Gaussian distribution on the real line: if
j
are independent random variables,
j
,
j
are nonzero constants such that
i
±
j
–1
j
0 for all i j and the conditional distribution of L
2=1 1 + ··· +
n
n
given L
1=1 1 + ··· +
n
n
is symmetric, then all random variables
j
are Gaussian. We prove some analogs of this theorem, assuming that independent random variables take on values in a finite Abelian group X and the coefficients
j
,
j
are automorphisms of X. 相似文献
5.
According to the well-known Heyde theorem the Gaussian distribution on the real line is characterized by the symmetry of the conditional distribution of one linear form of independent random variables given the other. We study analogues of this theorem for some locally compact Abelian groups X containing an element of order 2. We prove that if X contains an element of order 2, this leads to the fact that a wide class of non-Gaussian distributions on X is characterized by the symmetry of the conditional distribution of one linear form of independent random variables given the other. While coefficients of linear forms are topological automorphisms of a group.
相似文献6.
Ulrich Albrecht 《Results in Mathematics》2016,70(3-4):533-537
In this paper, we answer a question of R. Göbel and L. Fuchs by showing that there exits large classes of non-splitting mixed groups which have no non-trivial cellular covers. 相似文献
7.
M. V. Myronyuk 《Ukrainian Mathematical Journal》2004,56(10):1602-1618
We prove theorems that generalize the Skitovich-Darmois theorem to the case where independent random variables ξj, j = 1, 2, ..., n, n ≥ 2, take values in a locally compact Abelian group and the coefficients αj and βj of the linear forms L
1 = α1ξ1 + ... + αnξn and L
2 = β1ξ1 + ... + βnξn are automorphisms of this group.__________Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 56, No. 10, pp. 1342 – 1356, October, 2004. 相似文献
8.
A Step Beyond Kneser's Theorem for Abelian Finite Groups 总被引:1,自引:0,他引:1
9.
Let A be a finite-rank, torsion-free, self-small mixed abelian sp-group and let E(A) be the endomorphism ring of A. We give conditions for right and left heredity of E(A). A ring is right hereditary if each of its right ideals is projective. We also find the structure of one-sided ideals of E(A). 相似文献
10.
P. A. Krylov 《Siberian Mathematical Journal》2001,43(1):83-91
Let A be a finite-rank, torsion-free, self-small mixed abelian sp-group and let E(A) be the endomorphism ring of A. We give conditions for right and left heredity of E(A). A ring is right hereditary if each of its right ideals is projective. We also find the structure of one-sided ideals of E(A). 相似文献
11.
N. G. Khisamiev 《Algebra and Logic》2002,41(4):274-283
Let G be a completely decomposable torsion-free Abelian group and G= Gi, where G
i
is a rank 1 group. If there exists a strongly constructive numbering of G such that (G,) has a recursively enumerable sequence of elements g
i
G
i
, then G is called a strongly decomposable group. Let pi, i, be some sequence of primes whose denominators are degrees of a number p
i
and let
. A characteristic of the group A is the set of all pairs ‹ p,k› of numbers such that
for some numbers i
1,...,i
k
. We bring in the concept of a quasihyperhyperimmune set, and specify a necessary and sufficient condition on the characteristic of A subject to which the group in question is strongly decomposable. Also, it is proved that every hyperhyperimmune set is quasihyperhyperimmune, the converse being not true. 相似文献
12.
Ulrich Albrecht 《代数通讯》2013,41(11):3497-3511
13.
D. S. Chistyakov 《Russian Mathematics (Iz VUZ)》2018,62(7):47-52
We study abelian groups whose endomorphism rings are rings with unique addition. This means that there exists a unique binary operation of addition on the endomorphism semigroup which turns it into a ring. We also solve some close problems. 相似文献
14.
R. R. Andruszkiewicz 《代数通讯》2013,41(9):3760-3767
An abelian group is called a mixed one if it is neither torsion nor torsion-free. It is to be proved that every mixed group can be provided with a nonzero associative ring structure. Our methods of proofs are straightforward and elementary. 相似文献
15.
16.
Mixed Abelian groups with isomorphic endomorphism semigroups are studied. In particular, the question of when the isomorphism of endomorphism semigroups of Abelian groups implies the isomorphism of the groups themselves is investigated. 相似文献
17.
18.
Evelina Viada 《Journal of Number Theory》2005,112(1):67-115
In this article, we show how to modify the proof of the Abelian Subvariety Theorem by Bost (Périodes et isogénies des variétés abeliennes sur les corps de nombres, Séminaire Bourbaki, 1994-95, Theorem 5.1) in order to improve the bounds in a quantitative respect and to extend the theorem to subspaces instead of hyperplanes. Given an abelian variety A defined over a number field κ and a non-trivial period γ in a proper subspace W of tAK with K a finite extension of κ, the Abelian Subvariety Theorem shows the existence of a proper abelian subvariety B of , whose degree is bounded in terms of the height of W, the norm of γ, the degree of κ and the degree and dimension of A. If A is principally polarized then the theorem is explicit. 相似文献
19.
F. E. A. Johnson 《代数通讯》2013,41(5):2034-2047
Let G be a finite group with integral group ring Λ =Z[G]. The syzygies Ωr(Z) are the stable classes of the intermediate modules in a free Λ-resolution of the trivial module. They are of significance in the cohomology theory of G via the “co-represention theorem” Hr(G, N) = Hom𝒟er(Ωr(Z), N). We describe the Ωr(Z) explicitly for the dihedral groups D4n+2, so allowing the construction of free resolutions whose differentials are diagonal matrices over Λ. 相似文献
20.
S. Ya. Grinshpon 《Acta Appl Math》2005,85(1-3):143-146