Chapter

Rings characterized by their proper factor rings

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/9780199664511.003.0002

Series: Oxford Mathematical Monographs

Rings characterized by their proper factor rings

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Chapter 2 considers rings characterized by their proper factor rings. The first section studies rings each of whose proper factor rings is artinian. The next section deals with rings each of whose proper factor rings is perfect, a property that relatesto the existence of strong flat covers for commutative rings. The third section discusses nonprime rings each of whose proper factor rings is von Neumann regular. This chapter concludes by considering results due to Cohen and Levy for commutativerings for which every proper factor ring is self-injective — a property shared by Dedekind domains.

Keywords: factor rings; artinian rings; perfect rings; von Neumann regular rings

Chapter.  8321 words. 

Subjects: Algebra

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