This paper presents new results concerning the structure of \(SI\)-groups, and refines and purifies the results obtained in this field by Shalom Feigelstock ['Additive groups of rings whose subrings are ideals' Bull. Austral. Math. Soc. \(55\) (1997), 477-481]. The structure theorem describing torsion-free \(SI\)-groups is proved in the associative case. Numerous examples of \(SI\)-groups are given. Some inconsistencies in Feigelstock's article are noted and removed.

DOI:

 10.1017/S0004972714000641

Infinite Abelian groups

On SI -groups

Butler groups of infinite rank

It is determined exactly which classifiable C*-algebras have approximately inner flip. The answer includes a number of C*-algebras with torsion in their K-theory.

K-theoretic characterization of c*-algebras with approximately inner flip

w 2. Definitions and Notations We will follow the notations of Fuchs [I]. In the following let I be an arbitrary set and (a i )~2g for each ieI. Let I be well ordered beginning with the natural numbers. Then let 2g~=I-Ii~j(ai) be its cartesian power (=direct product, cf. Fuchs [I; p. 39]). If b~Z I, we denote by bi=n~(b).a~=n i .ag its component /e l ; c.f. Fuchs [I; p. 39, 94]. If be7l I, let o(b)= {ieI, hi:t:0 } be its support. If K is an ideal of the Boolean algebra B(I) of all subsets of I, then the K-direct sum of the (a~) is defined by @i((a~) = ( ~ ~g = {b~ 7Z', v(b)~K} ;

http://link.springer.com/content/pdf/10.1007/BF01214169.pdf

The characteristic subgroups of the Baer-Specker group

It is proved that if G is a compact connected Hausdorff group of uncountable weight, w(G), then G contains a homeomorphic copy of [0, 1]w(G). From this it is deduced that such a group, G, contains a homeomorphic copy of every compact Hausdorff group with weight w(G) or less. It is also deduced that every infinite compact Hausdorff group G contains a Cantor cube of weight w(G), and hence has [0, 1]w(G) as a quotient space.

Infinite Abelian groups

Citations

On SI -groups

Butler groups of infinite rank

K-theoretic characterization of c*-algebras with approximately inner flip

The characteristic subgroups of the Baer-Specker group

Compact groups and products of the unit interval

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