Multiplication Modules and characteristic submodules

  • Park, Young-Soo (Department of Mathematics, Kyungpook National University, Taegu 702-701) ;
  • Chol, Chang-Woo (Department of Mathematics Education, Taegu National University of Education, Taegu 705-715)
  • Published : 1995.08.01

Abstract

In this note all are commutative rings with identity and all modules are unital. Let R be a ring. An R-module M is called a multiplication module if for every submodule N of M there esists an ideal I of R such that N = IM. Clearly the ring R is a multiplication module as a module over itself. Also, it is well known that invertible and more generally profective ideals of R are multiplication R-modules (see [11, Theorem 1]).