Chapter

Rings characterized by their one‐sided ideals

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/9780199664511.003.0019

Series: Oxford Mathematical Monographs

Rings characterized by their one‐sided ideals

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This chapter deals with the dual notion of structure of rings determined by properties of its one-sided ideals. The first section deals with rings in which each right ideal is quasi-injective, equivalently, rings which are right self-injective and whose each essential right ideal is two-sided. Structure theorems due to Beidar, Byrd, Jain, Ivanov, Mohamed, etc, are included in this section. The second section deals with rings in which each right ideal is a finite direct sum of quasi-injective right ideals, a property shared by artinian serial rings as shown by Nakayama. The last four sections deal with rings in which each one-sided ideal is π-injective, weakly injective, quasi-projective or their direct sums.

Keywords: q-rings; Σ-q rings; quasi-injective; π-injective; weakly injective; quasi-projective

Chapter.  11373 words. 

Subjects: Algebra

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