Chapter

Rings each of whose simple modules is injective (or Σ‐injective)

S. K. Jain, Ashish K. Srivastava and Askar A. Tuganbaev

in Cyclic Modules and the Structure of Rings

Published in print September 2012 | ISBN: 9780199664511
Published online January 2013 | e-ISBN: 9780191746024 | DOI: http://dx.doi.org/10.1093/acprof:oso/9780199664511.003.0006

Series: Oxford Mathematical Monographs

Rings each of whose simple modules is injective (or Σ‐injective)

Show Summary Details

Preview

This chapter opens with Villamayor rings, that is, rings over which each simple module is injective. The second section discusses weakly V-rings, that is, rings over which every simple module is injective relative to proper cyclic modules. The next section deals with rings each of whose simple modules is Σ-injective that gives recent results due to Srivastava. Further generalizations are given in the fourth section that studies rings over which every simple module has the property that its injective hull is Σ-injective.

Keywords: simple modules; injective modules; Σ-injective modules; injective hull

Chapter.  9575 words. 

Subjects: Algebra

Full text: subscription required

How to subscribe Recommend to my Librarian

Buy this work at Oxford University Press »

Users without a subscription are not able to see the full content. Please, subscribe or login to access all content.