On the problem of splitting certain abelian extensions of splittable Abelian groups
نویسندگان
چکیده
منابع مشابه
On component extensions locally compact abelian groups
Let $pounds$ be the category of locally compact abelian groups and $A,Cin pounds$. In this paper, we define component extensions of $A$ by $C$ and show that the set of all component extensions of $A$ by $C$ forms a subgroup of $Ext(C,A)$ whenever $A$ is a connected group. We establish conditions under which the component extensions split and determine LCA groups which are component projective. ...
متن کاملsplitting of extensions in the category of locally compact abelian groups
let $pounds$ be the category of all locally compact abelian (lca) groups. in this paper, the groups $g$ in $pounds$ are determined such that every extension $0to xto yto gto 0$ with divisible, $sigma-$compact $x$ in $pounds$ splits. we also determine the discrete or compactly generated lca groups $h$ such that every pure extension $0to hto yto xto 0$ splits for each divisible group $x$ ...
متن کاملon component extensions locally compact abelian groups
let $pounds$ be the category of locally compact abelian groups and $a,cin pounds$. in this paper, we define component extensions of $a$ by $c$ and show that the set of all component extensions of $a$ by $c$ forms a subgroup of $ext(c,a)$ whenever $a$ is a connected group. we establish conditions under which the component extensions split and determine lca groups which are component projective. ...
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The design of decision procedures for combinations of theories sharing some arithmetic fragment is a challenging problem in verification. One possible solution is to apply a combination method à la Nelson-Oppen, like the one developed by Ghilardi for unions of non-disjoint theories. We show how to apply this non-disjoint combination method with the theory of abelian groups as shared theory. We ...
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It is proved that if A is an abelian p-group with a pure subgroup G so that A/G is at most countable and G is either p-totally projective or p-summable, then A is either p-totally projective or p-summable as well. Moreover, if in addition G is nice in A, then G being either strongly p-totally projective or strongly p-summable implies that so is A. This generalizes a classical result of Wallace ...
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ژورنال
عنوان ژورنال: Czechoslovak Mathematical Journal
سال: 1961
ISSN: 0011-4642,1572-9141
DOI: 10.21136/cmj.1961.100465