Chapter

Rings each of whose cyclic modules is injective (or CS)

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/9780199664511.003.0004

Series: Oxford Mathematical Monographs

Rings each of whose cyclic modules is injective (or CS)

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This chapter begins with the celebrated theorem of Osofsky that gives the structure of rings over which every cyclic module is injective, which was also considered by Skornyakov. The next section discusses a powerful result of Osofsky-Smith for rings over which each cyclic module satisfies the property that complement submodulesv are direct summands.

Keywords: cyclic modues; proper cyclic modules; injective modules; cS modules

Chapter.  4311 words. 

Subjects: Algebra

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