ON REDUCED MODULES AND RINGS

Abstract

In this paper we extend several results known for reduced rings to reduced modules. We prove that for a semiprime module or a module with zero Jacobson radical, the concepts of reduced, symmetric, ps-Armendariz and ZI modules coincide. New examples of reduced modules are furnished: flat modules over reduced rings and modules with zero Jacobson radical over left quo rings are reduced. Rings over which all modules are reduced/symmetric are characterized.

Keywords

• reduced modules, semiprime modules, ZI modules, ps-Armendariz modules

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22. Mangesh B. Rege*and A. M. Buhphang** Department of Mathematics, North Eastern Hill University, Permanent Campus, Shillong-793022, Meghalaya, India.
23. E-mails:*[e-mail] ,**[e-mail]