On mixed 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 $X\in\mathcal L$, let $E(X)$ denote the ring of continuous endomorphisms of $X$. In this paper, we determine for certain subclasses$\mathcal S$ of $\mathcal L$ the groups $X\in\mathcal S$ such that $E(X)$ is commutative. The main results concern the case of mixed LCA groups.

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

MSC: Primary 22B05; Secondary 22B05

Received: 25.10.2007

Language: English

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