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On torsionfree LCA groups with commutative rings of continuous endomorphisms

Valeriu Popa

Institute of Mathematics and Computer Science, Academy of Sciences of Moldova, Chişinău, Moldova

Abstract: Let $\mathcal L$ be the class of locally compact abelian (LCA) groups. For certain subclasses $\mathcal S$ of $\mathcal L$, we obtain information about the groups $X\in\mathcal S$ such that the ring $E(X)$ of continuous endomorphisms of $X$ is commutative. The main results concern torsionfree groups, groups with splitting torsion subgroups and their duals.

Keywords and phrases: LCA groups, ring of continuous endomorphisms, commutativity.

MSC: Primary 22B05; Secondary 16W80

Received: 11.10.2006

Language: English

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