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PURE-INJECTIVITY FROM A DIFFERENT PERSPECTIVE

Part of: Modules, bimodules and ideals

Published online by Cambridge University Press:  14 March 2017

S. R. LÓPEZ-PERMOUTH ,
J. MASTROMATTEO ,
Y. TOLOOEI  and
B. UNGOR
S. R. LÓPEZ-PERMOUTH
Affiliation:
Department of Mathematics, Ohio University, Athens, OH 45701, USA e-mails: lopez@ohio.edu, joseph.mastromatteo@gmail.com
J. MASTROMATTEO
Affiliation:
Department of Mathematics, Ohio University, Athens, OH 45701, USA e-mails: lopez@ohio.edu, joseph.mastromatteo@gmail.com
Y. TOLOOEI
Affiliation:
Department of Mathematics, Faculty of Science, Razi University, Kermanshah, 67149, Iran e-mail: y.toloei@razi.ac.ir
B. UNGOR
Affiliation:
Department of Mathematics, Ankara University, 06100 Ankara, Turkey e-mail: bungor@science.ankara.edu.tr
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Abstract

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The study of pure-injectivity is accessed from an alternative point of view. A module M is called pure-subinjective relative to a module N if for every pure extension K of N, every homomorphism N → M can be extended to a homomorphism K → M. The pure-subinjectivity domain of the module M is defined to be the class of modules N such that M is N-pure-subinjective. Basic properties of the notion of pure-subinjectivity are investigated. We obtain characterizations for various types of rings and modules, including absolutely pure (or, FP-injective) modules, von Neumann regular rings and (pure-) semisimple rings in terms of pure-subinjectivity domains. We also consider cotorsion modules, endomorphism rings of certain modules, and, for a module N, (pure) quotients of N-pure-subinjective modules.

MSC classification

Primary: 16D10: General module theory
Secondary: 16D80: Other classes of modules and ideals

Information

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 60 , Issue 1 , January 2018 , pp. 135 - 151
Copyright
Copyright © Glasgow Mathematical Journal Trust 2017 

References

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