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Title: On Some Classes of Hopfian Abelian Groups and Modules

Abstract

The hopficity property in a well-known class of Abelian groups—completely decomposable torsion-free groups—as well as in a class of modules over generalized matrix rings is studied. Examples of non-Hopfian completely decomposable torsion-free group are constructed.

Authors:
;  [1]
  1. Tomsk State University, Department of Algebra (Russian Federation)
Publication Date:
OSTI Identifier:
22771355
Resource Type:
Journal Article
Journal Name:
Journal of Mathematical Sciences
Additional Journal Information:
Journal Volume: 230; Journal Issue: 3; Conference: 5. All-Russian symposium on abelian groups, Biysk (Russian Federation), 20-25 Aug 2012; Other Information: Copyright (c) 2018 Springer Science+Business Media, LLC, part of Springer Nature; http://www.springer-ny.com; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 1072-3374
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICAL METHODS AND COMPUTING; GROUP THEORY; MATRICES; RINGS; TORSION

Citation Formats

Kaigorodov, E. V., E-mail: gazetaintegral@gmail.com, and Krylov, P. A., E-mail: krylov@math.tsu.ru. On Some Classes of Hopfian Abelian Groups and Modules. United States: N. p., 2018. Web. doi:10.1007/S10958-018-3745-9.
Kaigorodov, E. V., E-mail: gazetaintegral@gmail.com, & Krylov, P. A., E-mail: krylov@math.tsu.ru. On Some Classes of Hopfian Abelian Groups and Modules. United States. doi:10.1007/S10958-018-3745-9.
Kaigorodov, E. V., E-mail: gazetaintegral@gmail.com, and Krylov, P. A., E-mail: krylov@math.tsu.ru. Sun . "On Some Classes of Hopfian Abelian Groups and Modules". United States. doi:10.1007/S10958-018-3745-9.
@article{osti_22771355,
title = {On Some Classes of Hopfian Abelian Groups and Modules},
author = {Kaigorodov, E. V., E-mail: gazetaintegral@gmail.com and Krylov, P. A., E-mail: krylov@math.tsu.ru},
abstractNote = {The hopficity property in a well-known class of Abelian groups—completely decomposable torsion-free groups—as well as in a class of modules over generalized matrix rings is studied. Examples of non-Hopfian completely decomposable torsion-free group are constructed.},
doi = {10.1007/S10958-018-3745-9},
journal = {Journal of Mathematical Sciences},
issn = {1072-3374},
number = 3,
volume = 230,
place = {United States},
year = {2018},
month = {4}
}