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This article is cited in 22 scientific papers (total in 22 papers)
Abelian groups with normal endomorphism rings
A. R. Chekhlov Tomsk, RUSSIA
Abstract:
A ring is said to be normal if all of its idempotents are central. It is proved that a mixed group $A$ with a normal endomorphism ring contains a pure fully invariant subgroup $G\oplus B$, the endomorphism ring of a group $G$ is commutative, and a subgroup $B$ is not always distinguished by a direct summand in $A$. We describe separable, coperiodic, and other groups with normal endomorphism rings. Also we consider Abelian groups in which the square of the Lie bracket of any two endomorphisms is the zero endomorphism. It is proved that every central invariant subgroup of a group is fully invariant iff the endomorphism ring of the group is commutative.
Keywords:
fully invariant subgroup, central invariant subgroup, normal endomorphism ring, invariant endomorphism ring, Lie bracket of endomorphisms.
Received: 19.01.2009 Revised: 19.02.2009
Citation:
A. R. Chekhlov, “Abelian groups with normal endomorphism rings”, Algebra Logika, 48:4 (2009), 520–539; Algebra and Logic, 48:4 (2009), 298–308
Linking options:
https://www.mathnet.ru/eng/al411 https://www.mathnet.ru/eng/al/v48/i4/p520
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Abstract page: | 749 | Full-text PDF : | 102 | References: | 57 | First page: | 7 |
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