ON VON NEUMANN REGULAR MODULES

G. N. Sudharshana and D. Siva Kumar

  DOI:
  https://doi.org/10.37418/amsj.9.4.51

Full Text

Results gotten for a module $M$ over a commutative ring have been broadened to module over a ring which is not necessarily commutative. It has been indicated that an $R$-module $M$ is $VN$-regular module if and only if $M$ is a multiplication module and $R/(0 : M)$ is strongly regular ring. It has also been indicated that the notions of prime submodule, completely prime submodule, maximal submodule coincide in a strong symmetric $VN$-regular module.


Keywords:
Strongly regular ring, Module, Von Neumann regular element and module, strong symmetric module.