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Noncommutative Rings and Closure Operations on Submodules

  • Jesse ElliottEmail author
Chapter
Part of the Springer Monographs in Mathematics book series (SMM)

Abstract

Radicals and torsion theories, first introduced, respectively, by Maranda in 1962 [142] and Dickson and Lambek in 1966 [39, 129], are important tools for studying rings and their modules. In this chapter, we show that both are equivalent to certain functorial closure operations on submodules, and any “cohereditary” radical is completely determined by the closure operation it induces on left ideals.

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Department of MathematicsCalifornia State University, Channel IslandsCamarilloUSA

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