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Research articles

On LCA groups whose ring of continuous endomorphisms satisfies $DCC$ on closed ideals

Valeriu Popa

Institute of Mathematics and Computer Science, Academy of Sciences of Moldova, Academiei str. 5, MD-2028, Chişinău, Moldova

Abstract: We determine the structure of LCA (locally compact abelian) groups $X$ with the property that the ring $E(X)$ of continuous endomorphisms of $X$, taken with the compact-open topology, satisfies $DCC$ (descending chain condition) on different types of closed ideals.

Keywords and phrases: LCA groups, rings of continuous endomorphisms, DCC.

MSC: Primary 22B05; Secondary 16W80

Received: 25.05.2017

Language: English

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