A NOTE ON NILPOTENT MODULES OVER RINGS

P. Das

  DOI:
  https://doi.org/10.37418/amsj.9.4.37

Full Text

In this paper, we define nilpotent elements and nilpotent submodules of a module $M$ over a commutative ring $R$. We show that if $R$ has the ascending chain condition, then the singular submodule $Z(M)$ is nil a nil submodule of $M$. Also we prove that if $M$ is completely semi-prime module and the ring $R$ has the ascending chain condition (a.c.c) on annihilators, then $M$ contains no non-zero nil submodule.


Keywords:
Nilpotent elements of Modules, Nil submodules, Completely Semiprime modules, Singular submodule of a module.