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International Journal of Mathematics and Mathematical Sciences
Volume 20, Issue 3, Pages 529-538

Pure Baer injective modules

Department of Mathematics, Faculty of Science, Qatar University, Doha, Qatar

Received 19 April 1995; Revised 16 April 1996

Copyright © 1997 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


In this paper we generalize the notion of pure injectivity of modules by introducing what we call a pure Baer injective module. Some properties and some characterization of such modules are established. We also introduce two notions closely related to pure Baer injectivity; namely, the notions of a -pure Baer injective module and that of SSBI-ring. A ring R is an SSBI-ring if and only if every smisimple R-module is pure Baer injective. To investigate such algebraic structures we had to define what we call p-essential extension modules, pure relative complement submodules, left pure hereditary rings and some other related notions. The basic properties of these concepts and their interrelationships are explored, and are further related to the notions of pure split modules.