共查询到20条相似文献,搜索用时 15 毫秒
1.
Let C be an Abelian group. An Abelian group A in some class
of Abelian groups is said to be
C
H-definable in the class
if, for any group B\in
, it follows from the existence of an isomorphism Hom(C,A) Hom(C,B) that there is an isomorphism A B. If every group in
is
C
H-definable in
, then the class
is called an
C
H-class. In the paper, conditions are studied under which a class of completely decomposable torsion-free Abelian groups is a
C
H-class, where C is a completely decomposable torsion-free Abelian group. 相似文献
2.
Mathematical Notes - Let $$C$$ be an Abelian group. A class $$X$$ of Abelian groups is called a $$_CH $$ -class (a $$_CEH$$ -class) if, for any groups $$A$$ and $$B$$ in the class $$X$$ , the... 相似文献
3.
Mathematical Notes - Let $$\Lambda$$ be a class of Abelian groups. A group $$A\in\Lambda$$ is said to be determined by its endomorphism semigroup $$E^\star(A)$$ in the class $$\Lambda$$ if every... 相似文献
4.
K. S. Sorokin 《Journal of Mathematical Sciences》2014,197(5):655-657
Conditions for cleanness of endomorphism rings of completely decomposable Abelian groups are established. 相似文献
5.
E. A. Blagoveshchenskaya 《Journal of Mathematical Sciences》2014,197(4):467-478
A necessary and sufficient condition is found for rigid almost completely decomposable Abelian groups with p-primary regulator quotients to have endomorphism rings isomorphic to those of the corresponding groups with cyclic regulator quotients. 相似文献
6.
In the paper the concept of the similarity of homogeneously decomposable groups is introduced. One investigates the cases in which almost isomorphic groups are similar or isomorphic.
Mathematics Subject Classification (2000) 20K99. 相似文献
7.
V. K. Vildanov 《Journal of Mathematical Sciences》2014,197(5):590-594
In this paper, we consider the question of determinability of an Abelian group by its automorphism group in the class of completely decomposable block-rigid torsion-free Abelian groups. 相似文献
8.
9.
E. A. Blagoveshchenskaya 《Journal of Mathematical Sciences》2005,131(5):5948-5961
We prove that endomorphism rings of nearly isomorphic, almost completely decomposable groups of ring type are also nearly
isomorphic as additive structures. On this basis, acd groups can be considered in a dual connection with their endomorphism
rings.
__________
Translated from Sovremennaya Matematika i Ee Prilozheniya (Contemporary Mathematics and Its Applications), Vol. 13, Algebra,
2004. 相似文献
10.
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
11.
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
12.
V. Kh. Farukshin 《Journal of Mathematical Sciences》2014,197(5):684-687
A representation for p-local Abelian torsion-free groups of finite rank is obtained in terms of homomorphisms of p-adic modules of finite rank with fixed basis. 相似文献
13.
Some properties of fully transitive torsion-free groups are established. Necessary and sufficient conditions for full transitivity of quasihomogeneously decomposable torsion-free groups are obtained in terms of types. 相似文献
14.
《代数通讯》2013,41(7):2339-2350
ABSTRACT An abelian group is said to be minimal if it is isomorphic to all its subgroups of finite index. In this article we show that torsion-free groups which are complete in their ?-adic topology or are of p-rank not greater than 1, for all primes p, are minimal. A criterion is found for the minimality of all finite rank and for large classes of infinite rank completely decomposable groups. Separable minimal groups are also considered. 相似文献
15.
S. Ya. Grinshpon 《Acta Appl Math》2005,85(1-3):143-146
16.
17.
In the paper, Problem 18.3 of the book “Abelian groups” (2015) by L. Fuchs is solved in the case of Abelian groups with finite p-ranks. For an Abelian group A, a sequence of groups (An) is considered, where A0 = A and An+1 = End An. It is shown that, if all p-ranks of the group A are finite, then this sequence can stabilize either after A0 or after A1.
相似文献18.
Representations of posets in certain modules are used to find indecomposable almost completely decomposable torsion-free abelian groups. For a special class of almost completely decomposable groups we determine the possible ranks of indecomposable groups and show that the possible ranks are realized by indecomposable groups in the class. 相似文献
19.
Mathematical Notes - For an Abelian group $$A$$ , viewed as a module over its endomorphism ring $$E(A)$$ , the near-ring $$mathcal{M}_{E(A)}(A)$$ of homogeneous mappings is defined as the set of... 相似文献
20.
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