FUNDAMENTALNAYA I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

2011/2012, VOLUME 17, NUMBER 8, PAGES 59-61

Some classes of Hopfian Abelian groups

E. V. Kaygorodov

Abstract

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This paper describes the Hopfian groups in some classes of Abelian groups. The complete description of Hopfian divisible groups is presented; on the basis of this description, the study of Hopficity of arbitrary Abelian groups is reduced to the study of Hopficity of reduced groups. Direct sums of cyclic groups that are Hopfian groups are characterized. Finally, the paper looks at specific examples of rings whose additive groups are Hopfian.

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Last modified: March 23, 2013