You are in:Home/Publications/On modules which are subisomorphic to their pure-injective envelopes

Dr. Ahmed ali abd elaziz :: Publications:

On modules which are subisomorphic to their pure-injective envelopes
Authors: Maher Zayed, Ahmed A. Abdel-Aziz
Year: 2002
Keywords: Subisomorphic; pure-injective module; pure-semisimple ring; reduced product; axiomatisable class
Journal: Journal of Algebra and Its Applications
Volume: 1
Issue: 3
Pages: 289-294
Publisher: Not Available
Local/International: International
Paper Link: Not Available
Full paper Not Available
Supplementary materials Not Available

In the present paper, modules which are subisomorphic (in the sense of Goldie) to their pure-injective envelopes are studied. These modules will be called almost pure-injective modules. It is shown that every module is isomorphic to a direct summand of an almost pure-injective module. We prove that these modules are ker-injective (in the sense of Birkenmeier) over pure-embeddings. For a coherent ring R, the class of almost pure-injective modules coincides with the class of ker-injective modules if and only if R is regular. Generally, the class of almost pure-injective modules is neither closed under direct sums nor under elementary equivalence. On the other hand, it is closed under direct products and if the ring has pure global dimension less than or equal to one, it is closed under reduced products. Finally, pure-semisimple rings are characterized in terms of almost pure-injective modules.

Google ScholarAcdemia.eduResearch GateLinkedinFacebookTwitterGoogle PlusYoutubeWordpressInstagramMendeleyZoteroEvernoteORCIDScopus