On hereditarily and super R-Hopfian and L-co-Hopfian abelian groups. Issue 5 (4th May 2018)

• Record Type: Journal Article
• Authors: Goldsmith, Brendan; Gong, Ketao
• Is Part Of: Communications in algebra. Volume 46:Issue 5(2018)
• Page Start: 1889
• Page End: 1901
• Publication Date: 2018-05-04
• Subjects: Abelian groups -- co-Hopfian groups -- hereditarily R-Hopfian and L-co-Hopfian groups -- Hopfian groups -- super R-Hopfian and L-co-Hopfian groups; Primary 20K10 -- Secondary 20K21; Algebra -- Periodicals; 512.005
• DOI: 10.1080/00927872.2017.1360332
• Languages: English
• ISSNs: 0092-7872

Abstract

ABSTRACT: An Abelian group is said to be R-Hopfian [L-co-Hopfian] if every surjective [injective] endomorphism has a right [left] inverse. An Abelian group G is said to be hereditarily R-Hopfian [hereditarily L-co-Hopfian] if each subgroup of G is R-Hopfian [L-co-Hopfian]; similarly G is super R-Hopfian [super L-co-Hopfian] if each homomorphic image of G is R-Hopfian [L-co-Hopfian]. The various classes of hereditarily and super R-Hopfian and L-co-Hopfian groups are studied and necessary conditions for groups to have these properties are derived; in several, but not all, cases, sufficient conditions are also obtained.